CBSE Class 10 Mathematics Coordinate Geometry VBQs Set 01

Value Based Questions

Topic: Co ordinate Geometry

Class: X

Question. The distance between the points P(a sin ∅, 0) and Q (0, -a cos∅) is:
(a) 𝑎²
(b)1
(c) 2a
(d) a
Answer : D

Question. The Coordinates of the image of the point (-4,5) in Y-axis is:
(a) (4,5)
(b) (4, -5)
(c) (-4,-5)
(d) (0,5)
Answer : A

Question. If A and B are the points (-3,4) and (2,1) respectively , then the coordinates of the point C on AB produced such that AC = 2BC are:
(a)(2,4)
(b) (3,7)
(c) ( 7,-2)
(d) (7,-9)
Answer : C

Question. 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
Answer : D

Question. If four vertices of a parallelogram taken in order are (-3,-1), (a,b), (3,3) and (4,3), then a:b =
(a) 1:4
(b) 4:1
(c) 1:2
(d) 2:1
Answer : B

Short Answer Type Questions

Question. P (𝑥,−3) and Q(3 ,𝑦) are points of trisections the line segment joining A(7,−2) and B (1,−5), then find the values of 𝑥 and 𝑦
Answer : 𝑥=5,𝑦=−4

Question. Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units
Answer : y = 3, y = -9

Question. Find a relation between 𝑥 and 𝑦 such that the point (𝑥,𝑦) is equidistant from the points A(𝟑,𝟔) and B (−𝟑,𝟒)
Answer : 3𝑥+𝑦=5

Question. Show that the points (a,a) ,(-a,a) and (−√3 𝑎,√3 𝑎) are vertices of an equilateral triangle.
Answer : Do yourself

Question. Find the distance of the point P (−3,4) from the origin.
Answer : 5

Question. What is the mid-point of the line segment joining the points A (–2, 8) and B (– 6, – 4)?
Answer : -4,2)

Question. If P and Q are the points having coordinates (8,3) and (5,−1) respectively, then find the distance 3PQ
Answer : 15

Question. If P (𝑎2 ,4) is the mid-point of the line-segment joining the points A(−6,5) and B(−2,3), then find the value of 𝑎.
Answer : −8

Question. Find the third vertex of a triangle, if its two vertices are(-3,1) and (0,-2) and the centroid of this triangle is at origin.
Answer : (3,-1)

Question. If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p.
Answer : p= 7

Question. Find the value of p, so that the point (p, 2) divides the line- segment joining the points (2, 5) and (4, 7).
Answer : 𝑝=−(5/3)

Question. The length of a line segment is 10. If one end is at (2,− 3)and the abscissa of the second end is 10.
Find its ordinate.
Answer : 𝑦=3𝑜𝑟−9

CASE STUDY - 1

To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. Niharika runs the distance AD on the 2nd line and posts a green flag. Preet runs the distance AD on the eighth line and posts a red flag. (take the position of feet for calculation)

(i) What co-ordinates you will use for Green Flag?
Answer : (2, 25)

(ii) What is the distance between the green flag and the red flag?
Answer : √61

(iii) If Rashmi wants to post a blue flag adjacently in between these two flags. Where she will post a blue flag?
Answer : (6, 22.5)

CASE STUDY - 2

There is a function in the school. Ashima, Bharti and Camella are standing in a rectangular ground at points A, B and C respectively as shown in the figure. They are ready to perform an aerobic dance. –

(i) How far is Camella from y – axis?
Answer : 8

(ii) Find distance between Ashima and Bharti.
Answer : 3√2

(iii) Check whether AB + BC = AC?
Answer : Yes

Very Short Answer type Questions

Question. Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts.
Answer : (-1, 7/2), (0, 5), (1, 13/2)

Question. If the point P(k − 1, 2) is equidistant from the points A( 3, k) and B(k, 5), find the values of k.
Answer :1 and 5.

Question. Find the coordinates of the points of trisection of the line segment joining (4, –1) and (–2, –3).
Answer : (2, 5/3) (2, 7/3)

Question. Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units.
Answer : – 9, 3

Question. Find the point on y-axis which is equidistant from the points (−5, 2) and (9, −2).
Answer : (0, − 7).

Question. Mr. Gopal aged 70 lives in his house at (4,5). He goes to shop which is located at (5,2) and then to a park located at (3,6). 

a. Find the distance traveled by Mr. Gopal.

b. In what way will you take your grand father to the park? Why?

c. What are the values you exhibit when you accompany your grandfather?

Key points: Care for the Aged. Time management. Responsibility

Question. Three villages are located around the circle at (2,-1) (-3,2) and (-2,-4). A health center should be located at a point so that all three villages can reach the center in the same distance.

a. Find the point at which the health center can be located.

b. Do you agree with the decision of the Government that the doctors should work at least for two years in a village? Justify your answer.

Key Points; Social responsibility, Commitment, Empathy, Dedication.

Question. The end point of a town are (6,4) (6,2) and (2,4). A cyclone hits the town. 

a. Find the area damaged by the cyclone.

b. If you are a student of a locality, how will you help the people through your school Mention any two ways.

Key Points: Empathy, social responsibility, team work.

Question. A man has a triangular plot with the vertices (5,-5) (4,3) and (6,2). He divides in to three equal parts, one to his son and another to his daughter. The third part he located to child trust. 

a. What is the area of the land given to the child trust?

b. What are the values you learn from the man?

Key Points: Social responsibility, Care for for the children, generosity.

Question. A wood is cut from the tree with end points (5,2) and (3,1). A carpenter uses a part of it making furniture in the ratio 2:1. 

a. Find the point at which the carpenter cuts the wood.

b. If you are the person for ordering for the furniture, what would be your reaction as environment friendly

c. How will you avoid deforestation?

Key Points: Care for the environment, awareness or aforestation