📝 Coordinate Geometry (Question Bank)
Multiple Choice Questions
1. The distance of the point P (2, 3) from the x-axis is
(A) 2
(A) 2
(B) 3
(C) 1
(D) 5
Ans: (B)
2. The distance between the points A (0, 6) and B (0, –2) is
(A)6
(B) 8
(C) 4
(D) 2
Ans: (B)
3. The distance of the point P (–6, 8) from the origin is
(A) 8
(B) `2 sqrt7`
(C) 10
(D) 6
Ans: (C)
4. The distance between the points (0, 5) and (–5, 0) is
(A) 5
(B) `5 sqrt2`
(C) `2 sqrt5`
(D) 10
Ans: (B)
5. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is
(A) 5
(B) 3
(C) `sqrt34`
(D) 4
Ans: (C)
6. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(A) 5
(B) 12
(C) 11
(D) `7+ sqrt5`
Ans: (B)
7. The area of a triangle with vertices A (3, 0), B (7, 0) and C (8, 4) is
(A) 14
(B) 28
(C) 8
(D) 6
Ans: (C)
8. The points (–4, 0), (4, 0), (0, 3) are the vertices of a
(A) right triangle
(B) isosceles triangle
(C) equilateral triangle
(D) scalene triangle
Ans: (B)
9. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the
(A) I quadrant
(B) II quadrant
(C) III quadrant
(D) IV quadrant
Ans: (D)
10. The point which lies on the perpendicular bisector of the line segment joining the points A (–2, –5) and B (2, 5) is
(A) (0, 0)
(B) (0, 2)
(C) (2, 0)
(D) (–2, 0)
Ans: (A)
11. The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is
(A) (0, 1)
(B) (0, –1)
(C) (–1, 0)
(D) (1, 0)
Ans: (B)
12. If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then
(A) AP `=1/3`AB
(B) AP = PB
( C) PB `=1/3`AB
(D) AP `=1/2`AB
Ans: (D)
13. If `P (a/3, 4)` is the mid-point of the line segment joining the points Q (– 6, 5) and R (– 2, 3), then the value of a is
(A) – 4
(B) – 12
(C) 12
(D) – 6
Ans: (B)
14. The perpendicular bisector of the line segment joining the points A (1, 5) and B (4, 6) cuts the y-axis at
(A) (0, 13)
(B) (0, –13)
(C) (0, 12)
(D) (13, 0)
Ans: (A)
15. The coordinates of the point which is equidistant from the three vertices of the `triangleAOB` as shown in Fig. is
(A) `(x, y)`
(B) `(y, x)`
(C) `x/2, y/2`
(D) `y/2, x/2`
Ans: (A)
16. A circle is drawn with origin as the centre passes through `(13/2,0)`. The point which does not lie in the interior of the circle is
(A) `-3/4, 1`
(B) `2, 7/3`
(C) `5, -1/2`
(D) `-6, 5/2`
Ans: (D)
17. A-line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
(A) (0, – 5) and (2, 0)
(B) (0, 10) and (– 4, 0)
(C) (0, 4) and (– 10, 0)
(D) (0, – 10) and (4, 0)
Ans: (D)
18. The area of a triangle with vertices `(a, b + c), (b, c + a)`, and `(c, a + b)` is
(A) `(a + b + c)^2`
(B) 0
(C) `a + b + c`
(D) `abc`
Ans: (B)
19. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is
(A) 4 only
(B) ± 4
(C) – 4 only
(D) 0
Ans: (B)
20. If the points A (1, 2), O (0, 0), and C (a, b) are collinear, then
(A) `a = b`
(B) `a = 2b`
(C) `2a = b`
(D) `a = –b`
Ans: (C)
★★★★★★
Case Studies
CASE STUDY 1:
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 flower pots have been placed at a distance of 1 m from each other along with AD, as shown in the given figure below. Niharika runs `1/4` th the distance AD on the 2nd line and posts a green flag. Preet runs `1/5` th distance AD on the eighth line and posts a red flag.
1. Find the position of the green flag
a) (2, 25)
b) (2, 0.25)
c) (25, 2)
d) (0, -25)
2. Find the position of the red flag
a) (8, 0)
b) (20, 8)
c) (8, 20)
d) (8, 0.2)
3. What is the distance between both flags?
a) √41
b) √11
c) √61
d) √51
4. 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)
5. If Joy has to post a flag at one-fourth distance from the green flag, in the line segment joining the green and red flags, then where should he post his flag?
a) (3.5, 24)
b) (0.5, 12.5)
c) (2.25, 8.5)
d) (25, 20)
ANSWERS
1. a) (2, 25)
2. c) (8, 20)
3. c) √61
4. a) (5, 22.5)
5. a) (3.5, 24)
Case Study 2:
The class X students school in Krishnagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.
1. Taking A as origin, find the coordinates of P
a) (4, 6)
b) (6, 4)
c) (0, 6)
d) (4, 0)
2. What will be the coordinates of R, if C is the origin?
a) (8, 6)
b) (3, 10)
c) (10, 3)
d) (0, 6)
3. What will be the coordinates of Q, if C is the origin?
a) (6, 13)
b) (-6,13)
c) (-13, 6)
d) (13, 6)
4. Calculate the area of the triangles if A is the origin
a) 4.5
b) 6
c) 8
d) 6.25
5. Calculate the area of the triangles if C is the origin
a) 8
b) 5
c) 6.25
d) 4.5
ANSWERS:
1. a) (4, 6)
2. c) (10, 3)
3. d) (13, 6)
4. a) 4.5
5. d) 4.5
Case Study 3
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.
◘ Fullbacks: As shown by players H, I, and J.
◘ Goalie: As shown by player K
Using the picture of a hockey field below, answer the questions that follow:
1. The coordinates of the centroid of ΔEHJ are
(a) `(-2/3, 1)`
(b) `(1,-2/3)`
(c) `(2/3,1)`
(d) `( -2/3,-1)`
2. 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
(a) `(-3/2, 2)`
(b) `(2,-3/2)`
(c) `(2, 3/2)`
(d) `( -2,-3)`
3. The point on x-axis equidistant from I and E is
(a) `(1/2, 0)`
(b) `(0,-1/2)`
(c) `(-1/2,0)`
(d) `( 0,1/2)`
4. 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)`
(b) `(0,1)`
(c) `(-2,1)`
(d) `( -1,0)`
5. The point on y-axis equidistant from B and C is
(a) `(-1, 0)`
(b) `(0,-1)`
(c) `(1,0)`
(d) `( 0,1)`
Ans:
1 (d)
2 (c)
3 (a)
4 (b)
5 (d)
Q. Find the distance between the following pairs of points :
- `(a, b), (– a, – b)`
- `(a + b, a-b), (a - b, a + b)`
- `(a sin\alpha, a cos\alpha)`, `(a cos \alpha , -a sin\alpha)`
Q. Do the points `(3, 2), (–2, –3)`, and `(2, 3)` form a triangle? If so,
name the type of triangle formed.
Q. Show that the points `(1, 7), (4, 2), (–1, –1)`, and `(– 4, 4)` are the vertices of a square.
Q. Find a relation between x and y such that the point `(x, y)` is equidistant from the points `(7, 1)` and `(3, 5)`.
Q. Check whether (5, – 2), (6, 4), and (7, – 2) are the vertices of an isosceles triangle.
Q. Determine if the points (1, 5), (2, 3), and (– 2, – 11) are collinear.
Q. Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
Q. Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units.
Q. If Q(0, 1) is equidistant from P(5, –3) and R(x, 6), find the values of x. Also, find the distances QR and PR.
Q. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).
Q. Shows the arrangement of desks in a classroom. Neha, Shital, and Sharmila are seated at A(3, 1), B(6, 4), and C(8, 6) respectively. Do you think they are seated in a line? Give reasons for your answer.
Q. Find the centre of a circle passing through the points `(6, -6), (3, -7), and (3, 3)`.
Ans: `O (3, -2)`
Q. If the point `(x, y)` is equidistance from the points `(a + b, b-a)` and `(a-b, a+b)`, prove that `bx = ay`.
Q. If the points `A(x, 2), B(-3, -4)`, and `C(7, -5)` are collinear, then the value of `x` is ...........
Ans: `-63`
Q. The coordinates of the point which is equidistant from the three vertices of the `\triangle AOB` as shown in the Fig. is.....................
Ans: `(x,y)`
Q. `ABCD` is a parallelogram with vertices `A (x_1, y_1), B (x_2, y_2) and C (x_3, y_3)`. Find the coordinates of the fourth vertex `D` in terms of `x_1, x_2, x_3, y_1, y_2 and y_3`.
Ans: `(x_1 + x_3 – x_2 , y_1 + y_3 – y_2)`
Q. Find the area of the triangle ABC with A (1, –4) and the mid-points of sides through A being (2, – 1) and (0, – 1).
Ans: 12 sq. units
More questions will be updated soon.
Wow very nice 😃😃😃
ReplyDeleteThank you
DeleteVery
ReplyDeletecreatical questions paper
Thank you
DeleteVery important questions sir ✌👍
ReplyDeleteVery important and hard questions 👍
ReplyDeleteOutstanding questions
ReplyDeleteVery very hard and traf questions
Tanks for best questions select
👆👆👆🙏🙏🙏🙏🌏🌏🌏⛰⛰⛰🌐🌐🌐