Page 1 :
No. 2021/X/Ch.7/MCQ, , Name:, , Excel Educational Centre, AlThumama, , X, , MCQ–Coordinate Geometry, , ===================================================================================, 1. The values of 𝑦 for which the distance between the points 𝐴(3, −1) and 𝐵(11, 𝑦) is 10 units, are., (a) −5, 7, , (b) 5, −7, , (c) 11, 3, , (d) −1, 11., , 2. If the points 𝑃 (𝑘 − 1, 2) is equidistant from the points 𝐴(3, 𝑘) and 𝐵 (𝑘, 5), then the values of 𝑘 are, (a) 1, 8, , (b) 1, 5, , (c) 1, 4, , (d) None of these., , 3. The relation between 𝑥 and 𝑦 such that the point 𝑃 (𝑥, 𝑦) is equidistant from the points 𝐴(1, 4) and, 𝐵(−1, 2) is, (a) 𝑥 − 𝑦 + 3 = 0, , (b) 𝑥 = 𝑦, , (c) 𝑥 = 2𝑦, , (d) None of these., , 4. Find those points on 𝑥-axis, each of which is at a distance of 5 units from the point 𝐴(5, – 3)., (a) (0, 1), , (b) (−1, 0), , (c) (1, 0), , (d) (0, 9)., , 5. Find those points on the y-axis, each of which is at a distance of 13 units from the point 𝐴(– 5, 7)., (a) (1, 19), , (b) (2, 19), , (c) 0, 19), , (d) (1, 2).., , 6. The point on x-axis which is equidistant from the points (5, −2) and (−3, 2) is, (a) (0, 1), , (b) (−1, 0), , (c) (1, 0), , (d) (0, 9)., , 7. Find the coordinates of the point equidistant from three given points 𝐴(5, 1), 𝐵(−3, −7) and 𝐶 (7, −1)., (a) (−2, −4), , (b) (2, −4), , (c) (2, 4), , (d) (−2, 4)., , 8. Points 𝐴 (−1, 𝑦) and 𝐵 (5, 7)lie on a circle with centre 𝑂(2, −3𝑦).Find the values of 𝑦., (a) −1, 7, , (b) 1, −7, , (c) 2, 8, , (d) −2, −8., , 9. If the point (𝑥, 𝑦) is equidistant from the points (𝑎 + 𝑏, 𝑏 − 𝑎) and (𝑎 − 𝑏, 𝑎 + 𝑏), then, (a), , 𝑏, 𝑥, , =, , 𝑎, 𝑦, , (b) 𝑎𝑏 = 𝑥𝑦, , (c) 𝑎𝑥 = 𝑏𝑦, , (d) 𝑏𝑥 = 𝑎𝑦, , 10. The coordinates of the point which divides the line segment joining the points 𝐴(4 , −3 ) and 𝐵 (9, 7) in, the ratio 3: 2 is, (a) (−7, −3), , (b) (3, 7), , (c) (7, 3), , (d) None of these., , 11. The co-ordinates of the point P dividing the line segment joining the points A (1,3) and B (4,6) internally, in the ratio 2:1 are, (a) (2,4), , (b) (4,6), , (c) (4,2), , (d) (3,5)., , 12. The mid-point of (3𝑝, 4) and (−2,2𝑞) is (2,6) . Find the value of 𝑝 + 𝑞, (a) 5, , (b) 6, , (c) 7, , (d) 8., , 13. The distance of point A(-5, 6) from the origin is, (a) 11 units, , (b) 61 units, , (c) √11 units, , (d) √61 units, 2, , 14. The coordinates of a point P on the line segment joining 𝐴(1 , 2) and 𝐵(6, 7) such that 𝐴𝑃 = 𝐴𝐵., 5, , (a) (3, −4), , (b) (3, 4), , (c) (−3, −4), , (d) (−3, 4)., , 15. Point 𝑃 divides the line segment joining the points 𝐴(2 , 1) and 𝐵(5, −8) such that, , 𝐴𝑃, 𝐴𝐵, , 1, , = . If 𝑝 lies on the, 3, , line 2𝑥 − 𝑦 + 𝑘 = 0, then the value of 𝑘., (a) −2, , (b) 2, , (c) 4, , (d) −4., , 16. In what ratio does the point (– 4, 6) divide the line segment joining the points 𝐴(– 6, 10) and 𝐵(3, – 8)?, (a) 7: 1, , (b) 7: 2, , (c) 2: 7, , (d) 1: 7, , Excel Educational Centre, Villa #25, Street #818, Al Thumama, Doha, Qatar. Web:www.excelqatar.org,, Email:[email protected]. Ph: 00974 7070 7445, 00974 4476 2232, Page 1 of 8

Page 2 :
17. Find the ratio in which the point 𝑃(𝑥, 2) divides the line segment joining the points 𝐴(12, 5) and, 𝐵(4, −3). Also find the value of 𝑥., (a) 3: 5, 𝑥 = 9, , (b) 5: 3, 𝑥 = −9, , (c) 2: 3, 𝑥 = 8, , (d) 3: 2, 𝑥 = −8., , 18. Point M 11, y lies on the line segment joining the points P15, 5, Q9, 20 . Find the ratio in which point, M divides the line segment PQ and also find the value of ' y ' ., (a) 1: 3, 𝑦 = 4, , (b) 2: 1, 𝑦 = 9, , (c) 1: 2, 𝑦 = −9, , (d) None of these., , 19. If the point 𝑃 (−1, 2) divides the line segment joining the points 𝐴(2, 5) and 𝐵(𝑥, 𝑦) in the ratio 3: 4, then, the value of 𝑥 2 + 𝑦 2 is, (a) −7, , (b) 7, , (c) 29, , (d) −29, , 20. If P(9𝑎 − 2, −𝑏) divides line segment joining 𝐴(3𝑎 + 1, −3) and 𝐵(8𝑎, 5) in the ratio 3: 1, find the values, of 𝑎 and 𝑏., (a) 𝑎 = 1, 𝑏 = −, , 13, 4, , (b) 𝑎 = −1, 𝑏 =, , 13, 4, , (c) 𝑎 = −, , 13, 4, , ,𝑏 = 1, , (d) 𝑎 =, , 13, 4, , , 𝑏 = −1., , 21. The three vertices of a parallelogram 𝐴𝐵𝐶𝐷 taken in order are 𝐴(3, −4), 𝐵 (−1, −3) and 𝐶 (−6, 2). Then, the coordinates of the fourth vertex 𝐷 is, (a) (−2, 1), , (b) (−2, 1), , (c) (1, −2), , (d) (1, 2)., , 22. If(3, 3), (6, 𝑦), (𝑥, 7)and (5, 6) are the vertices of a parallelogram taken in order, find the values of 𝑥 and, 𝑦., (a) 𝑥 = −4, 𝑦 = −8, , (b) 𝑥 = −8, 𝑦 = −4, , (c) 𝑥 = 4, 𝑦 = 8, , (d) 𝑥 = 8, 𝑦 = 4., , 23. The vertices of a parallelogram in order are 𝐴(1,2), 𝐵(4, 𝑦), 𝐶(𝑥, 6) and 𝐷(3,5). Then (𝑥, 𝑦) is, (a) (6, 3), , (b) (3, 6), , (c) (5, 6), , (d) (1, 4), , 24. The equation of the perpendicular bisector of line segment joining points 𝐴(4,5) and 𝐵(−2,3) is, (a) 2𝑥 – 𝑦 + 7 = 0, , (b) 3𝑥 + 2 𝑦 – 7 = 0 (c) 3𝑥 – 𝑦 – 7 = 0, , (d) 3𝑥 + 𝑦 – 7 = 0, , 25. Point P divides the line segment joining 𝑅(−1, 3) and 𝑆(9,8) in ratio 𝑘: 1. If P lies on the line 𝑥 – 𝑦 + 2 =, 0, then value of 𝑘 is, 2, , (a) 3, , 1, , (b) 2, , 1, , (c) 3, , 1, , (d) 4, , 26. The centroid of ∆𝐴𝐵𝐶 whose vertices are 𝐴(−3, 0), 𝐵(5, −2) and 𝐶 (−8, 5)., (a) (−2, 1), , (b) (−2, 1), , (c) (1, −2), , (d) (1, 2)., , 27. Two vertices of a triangle are (3, −5) and (−7, 4). If its centroid is (2, −1), then the third vertex is, (a) (−2, −10), , (b) (2, 10), , (c) (10, 2), , (d) (−10, 2)., , 28. Points 𝑃, 𝑄, 𝑅 and 𝑆 divide the line segment joining the points 𝐴(1, 2) and 𝐵(6, 7) in 5 equal parts. Then, the coordinates of the point 𝑅 is, (a) (2, 3), , (b) (3, 4), , (c) (4, 5), , (d) (5, 6)., , 29. If two adjacent vertices of a parallelogram are (3, 2) and (– 1, 0) and the diagonals intersect at, (2, – 5) then find the coordinates of the other two vertices., (a) (1, −12), (5, −10), , (b) (−1, 12), (−10, 5) (c) (−12, 1), (−10, 5) (d) None of these., , 30. The distance of the point 𝑃(– 6, 8) from the origin is, `(a) 8, , (b) 2√7, , (c) 6, , (d) 10., , (c) 4, , (d) 5., , 31. The distance of the point (–3, 4) from x-axis is, (a) 3, , (b) –3, , Excel Educational Centre, Villa #25, Street #818, Al Thumama, Doha, Qatar. Web:www.excelqatar.org,, Email:[email protected]. Ph: 00974 7070 7445, 00974 4476 2232, Page 2 of 8

Page 3 :
32. If 𝑅(5, 6 ) is the midpoint of the line segment 𝐴𝐵 joining the points 𝐴(6 , 5 ) and 𝐵(4, 4), then 𝑦 equals, (a) 5, , (b) 7, , (c) 12, , (d) 6, , 33. The perimeter of the triangle with vertices (0, 4), (0, 0) and (3, 0) is, (a) 7 + √5, , (b) 5, , (c) 10, , (d) 12, , 𝑎, , 34. If 𝑃 ( , 4) is the midpoint of the line segment joining the points 𝐴(−6, 5) and 𝐵(−2, 3), then the value of 𝑎, 2, , is, (a) –8, , (c) –4, , (b) 3, , (d) 4, , 35. If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are, (– 2, 5), then the coordinates of the other end of the diameter are, (a) (–6, 7), , (b) (6, –7), , (c) (4, 2), , (d) (5, 3), , 36. The point P which divides the line segment joining the points A(2, –5) and B(5, 2) in the ratio 2 : 3 lies in, the quadrant, (a) I, , (b) II, , (c) III, , (d) IV, , 37. If 𝑃(– 1, 1) is the midpoint of the line segment joining 𝐴(– 3, 𝑏) and 𝐵 (1, 𝑏 + 4), then 𝑏 =, (a) 1, , (b) –1, , (c) 2, , (d) 0, , 38. The line 2𝑥 + 𝑦 − 8 = 0 divides the line segment joining 𝐴(2, – 2) and 𝐵(3 ,7) in the ratio, (a) 2 : 5, , (b) 2 : 9, , (c) 2 : 7, , (d) 2 : 3, , 39. The points (1, 7), (4, 2), (–1, –1) and (– 4, 4) are the vertices of a square., (a) square, , (b) rectangle, , (c) rhombus, , (d) None, , 40. The midpoint 𝑃 of the line segment joining the points 𝐴(−10 , 4) and 𝐵(−2 ,0)lie on the line segment, joining the points 𝐶 (−9, −4) and 𝐷(−4, 𝑦). Find the ratio in which 𝑃 divides 𝐶𝐷. Also find the value of 𝑦., (a) 1: 2, 𝑦 = −4, , (b) 2: 3, 𝑦 = −6, , (c) 3: 2, 𝑦 = 6, , (d) 2: 1, 𝑦 = 4., , Case Study Questions, 1. A hockey field is the playing surface for the game of hockey. Historically, the game was, played on natural turf (grass) but nowadays it is predominantly played on an artificial turf. It is, rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed, equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The, inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the, crossbar must be 2.14 metres (7 feet) above the ground. Each team plays with 11 players on, the field during the game including the goalie. Positions you might play include, , Forward: As shown by players A, B, C and D., , , , Midfielders: As shown by players E, F and G., , , , Defenders: As shown by players H, I and J., , , , Goal Keeper: As shown by player K Using the picture of a hockey field below, answer the, questions that follow:, , Excel Educational Centre, Villa #25, Street #818, Al Thumama, Doha, Qatar. Web:www.excelqatar.org,, Email:[email protected]. Ph: 00974 7070 7445, 00974 4476 2232, Page 3 of 8

Page 4 :
i) The coordinates of the centroid of ΔEHJ are, 2, , (a) (− 3 , 1), , 2, , (b) (1, − 3), , 2, , (c) (3 , 1), , 2, , (d) (− 3 , −1), , ii) If a player P needs to be at equal distances from A and G, such that A, P and G are in, straight line, then position of P will be given by, 3, , (a) (− 2 , 2), , 3, , (b) (2, − 2), , 3, , (c) (2, 2 ), , (d) (−2, −3), , iii) The point on 𝑥 axis equidistant from I and E is, 1, , (a) (2 , 0), , 1, , (b) (0, − 2), , 1, , (c) (− 2 , 0 ), , 1, , (d) (0, 2 ), , iv) What are the coordinates of the position of a player Q such that his distance from K is, twice his distance from E and K, Q and E are collinear?, (a) (1, 0), v), , (b) (0,1), , (c) (−2,1 ), , (d) (−1,0), , The point on 𝑦 axis equidistant from B and C is, (a) (−1, 0), , (b) (0, −1), , (c) (1,0 ), , (d) (0,1), , 2. Pacific Ring of Fire, The Pacific Ring of Fire is a major area in the basin of the Pacific Ocean where many, earthquakes and volcanic eruptions occur. In a large horseshoe shape, it is associated with a, nearly continuous series of oceanic trenches, volcanic arcs, and volcanic belts and plate, movements., https://commons.wikimedia.org/wiki/File:Pacifick%C3%BD_ohniv%C3%BD_kruh.png, , Excel Educational Centre, Villa #25, Street #818, Al Thumama, Doha, Qatar. Web:www.excelqatar.org,, Email:[email protected]. Ph: 00974 7070 7445, 00974 4476 2232, Page 4 of 8

Page 5 :
Fault Lines, Large faults within the Earth's crust result from the action of plate tectonic forces, with the, largest forming the boundaries between the plates. Energy release associated with rapid, movement on active faults is the cause of most earthquakes., , https://commons.wikimedia.org/wiki/File:Faults6.png, , Based on the given information, answer the questions, i) The distance between the point Country A and Country B is, (a) 4 units, , (b) 5 units, , (c) 6 units, , (d) 7 units., , ii) Find a relation between 𝑥 and 𝑦 such that the point (𝑥, 𝑦) is equidistant from the Country C, and Country D., (a) 𝑥 − 𝑦 = 2, (b) 𝑥 + 𝑦 = 2, (c) 2𝑥 − 𝑦 = 0, (d) 2𝑥 + 𝑦 = 2., iii) The fault line 3𝑥 + 𝑦 – 9 = 0 divides the line joining the Country 𝑃(1, 3) and Country, 𝑄(2, 7) internally in the ratio, (a) 3 : 4, (b) 3 : 2, (c) 2 : 3, (d) 4 : 3, iv) The distance of the Country M from the 𝑥-axis is, (a) 1 units, v), , (b) 2 units, , (c) 3 units, , (d) 5 units, , What are the co-ordinates of the Country lying on the mid-point of Country A and Country, D?, (a) (1, 3), , 9, , (b) (2, 2), , 5, , (c) (4, 2), , 9, , (d) (2 , 2), , Excel Educational Centre, Villa #25, Street #818, Al Thumama, Doha, Qatar. Web:www.excelqatar.org,, Email:[email protected]. Ph: 00974 7070 7445, 00974 4476 2232, Page 5 of 8

Page 6 :
3. Class X students of a secondary school in Krishnagar have been allotted a rectangular plot of, a land for gardening activity. Sapling of Gulmohar are planted on the boundary at a distance, of 1m from each other. There is a triangular grassy lawn in the plot as shown in the fig. The, students are to sow seeds of flowering plants on the remaining area of the plot., , Considering A as origin, answer question (i) to (v), i) What are the coordinates of A?, a) (0, 1), , b) (1, 0), , c) (0, 0), , d) (-1, -1), , c) (4, 5), , d) (5, 4), , c) (6, 0), , d) (7, 4), , c) (0, 16), , d) (16, 1), , ii) What are the coordinates of P?, a) (4,6), , b) (6, 4), , iii) What are the coordinates of R?, a) (6, 5), , b) (5, 6), , iv) What are the coordinates of D?, a) (16, 0), , b) (0, 0), , v) What is the coordinate of P if D is taken as the origin?, a) (12, 2), , b) ( -12, 6), , c) (12, 3), , d) (6, 10), , 4. Students of a school are standing/seating in rows and columns in their playground for Yoga, practice. A, B, C and D are the positions of four students as shown in the figure., , i) The positions of A, B respectively are:, , a) (3, 5), (8, 7), , b) (3, 5), (9, 7), , c) (3, 5), (7, 9), , d)(5, 3), (7, 9), , Excel Educational Centre, Villa #25, Street #818, Al Thumama, Doha, Qatar. Web:www.excelqatar.org,, Email:[email protected]. Ph: 00974 7070 7445, 00974 4476 2232, Page 6 of 8

Page 7 :
ii) The distance between A and B is:, a) √32 units, , b) √23 units, , d) √35., , c) √42, , iii) It is possible to place Jaspal in the drill in such a way that he is equidistant from each of, , the four students A, B, C and D then the Position of Jaspal is:, a) (3, 7), , b) (3, 5), , c) (5, 7), , d) (7, 5), , c) 4 units, , d) √32 Units, , c) (5, 11), (7, 9), , d) (11, 7), (5, 9)., , iv) The distance between A and C is, a) 8 units, , b) 6 units, , v) The positions of C and B respectively are:, , a) (11, 5), (9, 7), , b) (11, 5), (7, 9), , 5. Ajay, Bhigu and Colin are best friends since childhood. They always want to sit in a, row in the classroom . But teacher doesn’t allow them and rotate the seats row-wise every, day. Bhigu is very good in maths and he does distance calculation every day. He consider, the centre of class as origin and marks their position on a paper in a co-ordinate system. One, day Bhigu make the following diagram of their seating position., , i), , What is the coordinate of point A?, , a) (2, 2 ), , b) (2, −2 ), , c) (−2, 2 ), , d) (−2, −2 ), , ii) What is the distance of the point A from the origin, , a) 8, , b) 2√2, , c) 4, , d) 4√2, , c) √17, , d) 2√5, , iii) What is the distance between A and B?, , a) 3√19, , b) 3√5, , iv) A point D lies on the line segment between points A and B such that 𝑨𝑫: 𝑫𝑩 = 𝟒: 𝟑., , What is the coordinate of point D?, 10 2, , a) ( 7 , 7 ), , 2, , b) (7 , 1), , c) (−, , 10, 7, , 2, , ,−7 ), , 2, , d) (− 7 , −1 ), , v) What is the distance between B and C?, , a) 3√19, , b) 3√5, , c) 2√17, , d) 2√5, , Excel Educational Centre, Villa #25, Street #818, Al Thumama, Doha, Qatar. Web:www.excelqatar.org,, Email:[email protected]. Ph: 00974 7070 7445, 00974 4476 2232, Page 7 of 8

Page 8 :
6. In order to conduct Sports Day activities in your School, lines have been drawn with chalk, powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flowerpots, have been placed at a distance of 1 m from each other along AD, as shown in, 1, , given figure below. Niharika runs 4 th the distance AD on the 2nd line and posts a green, 1, , flag. Preet runs 5 th distance AD on the eighth line and posts a red flag., , i), , Find the position of green flag, , a) (2, 25 ), , b) (2, 0.25 ), , c) (25, 2 ), , d) (0, −25 ), , c) (8, 20 ), , d) (8, 0.2 ), , ii) Find the position of red flag, , a) (8, 0 ), , b) (20, 8 ), , iii) What is the distance between both the flags?, , a) √41, , b) √11, , c) √61, , d) √51., , iv) If Rashmi has to post a blue flag exactly halfway between the line segment, , joining the two flags, where should she post her flag?, a) (5, 22.5 ), , b) (10, 22), , c) (2, 8.5 ), , d) (2.5, 20), , v) If Joy has to post a flag at one-fourth distance from green flag ,in the line, , segment joining the green and red flags, then where should he post his flag?, a) (3.2, 24), , b) (3.5, 23.75), , c) (25, 20 ), , d) (2.25, 8.5), , ===========================================================================================, Prepared By : Abdurahiman K, Faculty Of mathematics, , Excel Educational Centre, Villa #25, Street #818, Al Thumama, Doha, Qatar. Web:www.excelqatar.org,, Email:[email protected]. Ph: 00974 7070 7445, 00974 4476 2232, Page 8 of 8