CBSE Class 10 Mathematics Coordinate Geometry MCQs Set 06

Question. The points (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0) forms a quadrilateral of type:
(a) Square
(b) Rectangle
(c) Parallelogram but not rectangle
(d) Rhombus but not square

Answer: A

Question. If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:
(a) 2
(b) -2
(c) 1
(d) -1

Answer: A

Question. The Point (-1,-2) lies on
(a) x-y =1
(b) 2x =y
(c) x +y= -3
(d) All of the options

Answer: D

Question. The distance of point A(2, 4) from x-axis is
(a) 2 units
(b) 4 units
(c) -2 units
(d) -4 units

Answer: B

Question. Equation of X-axis is is
(a) x=0
(b) y=k
(c) x=k
(d) None of the options

Answer: D

Question. If O(p/3, 4) is the midpoint of the line segment joining the points P(-6, 5) and Q(-2, 3). The value of p is:
(a) 7/2
(b) -12
(c) 4
(d) -4

Answer: B

Question. The point which divides the line segment of points P(-1, 7) and (4, -3) in the ratio of 2:3 is:
(a) (-1, 3)
(b) (-1, -3)
(c) (1, -3)
(d) (1, 3)

Answer: D

Question. The ratio in which the line segment joining the points P(-3, 10) and Q(6, – 8) is divided by O(-1, 6) is:
(a) 1:3
(b) 3:4
(c) 2:7
(d) 2:5

Answer: C

Question. The coordinates of a point P, where PQ is the diameter of a circle whose centre is (2, – 3) and Q is (1, 4) is:
(a) (3, -10)
(b) (2, -10)
(c) (-3, 10)
(d) (-2, 10)

Answer: A

Question. The area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1) taken in order, is:
(a) 12 sq.units
(b) 24 sq.units
(c) 30 sq.units
(d) 32 sq.units

Answer: B

Question. The distance of the point P(–6, 8) from the origin is
(a) 8 units
(b) 2√7 units
(c) 10 units
(d) 6 units

Answer: C

Question. The distance between the points (0, 5) and (–5, 0) is
(a) 5 units
(b) 5√2 units
(c) 2√5 units
(d) 10 units

Answer: B

Question. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5
(b) 12
(c) 11
(d) 7 + √5

Answer: B

Question. 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)

Answer: A

Question. 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

Answer: C

Question. The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio
(a) 3 : 4
(b) 3 : 2
(c) 2 : 3
(d) 4 : 3

Answer: A

Question. The points (1,1), (-2, 7) and (3, -3) are
(a) vertices of an equilateral triangle
(b) collinear
(c) vertices of an isosceles triangle
(d) none of the options

Answer: B

(CASE STUDY BASED QUESTIONS)

1. One day Ram went to his home town during Dussehra vacation.During his excursion, he noted the four places Temple, TV tower, Mall and School, then he tried to locate all the places using graph sheet by taking his position at origin.He marked A,B,C and D for school,TV Tower,Temple and Mall respectively on the graph sheet by taking scale as I Unit = 1 km as shown below.

Question. Find the co-ordinates of C.
a) (0,-1)
b) (8,3)
c) (6,7)
d) (-2,3)

Answer: C

Question. Find the distance between School and TV Tower.
a) 4km
b) 4√5 km
c) 2√5 km
d) 3√5 km

Answer: B

Question. Find the distance between T.V Tower and Mall.
a) 8km
b) 10km
c) 6km
d) 9 km

Answer: B

Question. Find the distance between School and Temple.
a) 8km
b) 10km
c) 6km
d) 9 km

Answer: B

Question. Name the quadrilateral so formed.
a) Square
b) Rectangle
c) Rhombus
d) None of these

Answer: B

2. To conduct sports day activities, in your rectangular shaped school groundABCD, lines have been drawn with chalk powder at a distance of 1m each.100 flower pots have been placed at a distance of 1m from each other along AD,as shown in the below figure. Niharika runs 1 4th distance AD on the 2nd line and posts a green flag.Preet runs 1 5th distance AD on the 8th line and posts a red flag.

Question. At what distance Niharika posted the green flag from the starting point of second line?
a) 20m
b) 25 m
c) 100m
d) 50m

Answer: B

Question. At what distance Preet posted the red flag from the starting point of 8th line?
a) 20m
b) 25 m
c) 100m
d) 50m

Answer: A

Question. What is the distance between both the flags?
a) √61 m
b) √101m
c) √51m
d) √11m

Answer: A

Question. If Rashmi has to post a blue flag exactly halfway between the line segments joining the twoflags.Where should she post her flag ?
a) (5,5)
b) (22.5,5)
c) (5,22.5)
d) None of these

Answer: C

Question. If Swetha has to post a blue flag exactly halfway between the line segments joining the point A and green flag. Where should she post her flag ?
a) (1,5)
b) (12.5,1)
c) (1,22.5)
d) (1,12.5)

Answer: D

3. (Covid-19 vaccination) Mr. Jaskirat Singh is living in Jalandhar Punjab. As per the government he takes his dose of vaccine in the months of June 2021 in the Civil Hospital Jalandhar. Now he want to take his second dose. The following map is showing three vaccination centres near his home. O represents his home. Observe this condition and answer the following questions. Vaccination centre A, B & C as shown in the figure.

Question. The coordinates of nearest vaccination centre.
a) (3, 1)
b) (4, 2)
c) (0, 4)
d) (7, 4)

Answer: A

Question. According to the figure vaccination centre B is divide the line joining vaccination centre A to C
a) 2 :3
b) 3:1
c) 3: 2
d) 1 :1

Answer: C

Question. Distance between centre A to C
a) 4√2
b) 5√2
c) 41√2
d) 50

Answer: B

Question. Assuming he went to centre B and doses are finished. Then what is the closestdistance he has to cover to reach another Vaccination centre.
a) 4√2
b) √2
c) 2√2
d) 6√2

Answer: C

Question. Straight distance between his home to Vaccination centre C is
a) 11
b) 12
c) 13
d) 10

Answer: D

4. Kushal is a class X student residing in a village. Oneday, he went to a city Hospital along with his grandfather for general check-up. From there he visited three places -School, Library and Police station. After returning to his village, he plotted a graph by taking Hospital as origin and marked three places on the graph as per his direction of movement and distance. The graph is shown below.

Question. What are the coordinates of library?
a) (6,2)
b) (2,6)
c) (2,-1)
d) (2,3)

Answer: A

Question. Distance between school and hospital is(in units)
a) √11
b) √13
c) √5
d) √17

Answer: B

Question. Distance between school and police station is(in units)
a) 4
b) 3
c) 2
d) 1

Answer: A

Question. Distance between police station and hospital is(in units)
a) 2
b) √5
c) √7
d) 3.5

Answer: B

Question. Nearest place to hospital is
a) Police station
b) school
c) hospital
d) all are at equal distance

Answer: A

5. 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 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.

Question. Taking A as origin, find the coordinates of P
a) (4, 6)
b) (6, 4)
c) (0, 6)
d) (4, 0)

Answer: A

Question. What will be the coordinates of mid-point of side QR if A is the origin?
a) (8, 6)
b) (9/2, 7/2)
c) (7/2, 3)
d) (7/2, 9/2)

Answer: B

Question. Mid-point of PR, if A is the origin?
a) (5, 11/2)
b) (-6, 13)
c) (-13, 6)
d) (13, 6)

Answer: A

Question. Length of side PQ if A is origin is
a) √24
b) √17
c) √62
d) 25

Answer: B

Question. The length of side QR as A is origin is
a) 8
b) 3√2
c) 2√3
d) 4.5

Answer: B