CBSE Class 10 Mathematics Coordinate Geometry Assignment Set 03

Question. In what ratio is the line segment joining the points (3, 5) & (–4, 2) divided by y–axis?
(a) 3 : 2
(b) 3 : 4
(c) 2 : 3
(d) 4 : 3

Answer: B

Question. The point P on x-axis equidistant from the points A(–1, 0) and B(5, 0) is
(a) (2, 0)
(b) (0, 2)
(c) (3, 0)
(d) (2, 2)

Answer: A

Question. The coordinates of the point which is reflection of point (–3, 5) in x-axis are
(a) (3, 5)
(b) (3, –5)
(c) (–3, –5)
(d) (–3, 5)

Answer: C

Question. P, Q, R are three collinear points. The coordinates of P and R are (3, 4) and (11, 10) respectively and PQ is equal to 2.5 units. Coordinates of Q are
(a) (5, 11/2)
(b) (11, 5/2)
(c) (5, –11/2)
(d) (–5, 11/2)

Answer: A

Question. C is the mid-point of PQ, if P is (4, x), C is (y, –1) and Q is (–2, 4), then x and y respectively are
(a) – 6 and 1
(b) – 6 and 2
(c) 6 and – 1
(d) 6 and – 2

Answer: A

Question. The distances of a point from the x-axis and the y-axis are 5 and 4 respectively. The coordinates of the point can be
(a) (5, 4)
(b) (5, 0)
(c) (0, 4)
(d) (4, 5)

Answer: D

Question. Which of the following is / are not correct ?
Three points will form :
(a) an equilateral triangle, if all the three sides are equal.
(b) an isosceles triangle, if any two sides are equal.
(c) a collinear or a line, if sum of two sides is equal to third side.
(d) a rhombus, if all the four sides are equal.

Answer: D

Question. The centre of the circle passing through the ponts (6, – 6), (3, – 7) and (3, 3) is
(a) (3, 2)
(b) (–3, –2)
(c) (3, – 2)
(d) (–3, 2)

Answer: C

Question. A circle passes through the vertices of a triangle ABC.
If the vertices are A(–2, 5), B(–2, –3), C(2, –3), then the centre of the circle is
(a) (0, 0)
(b) (0, 1)
(c) (–2, 1)
(d) (0, –3)

Answer: B

Question. Find the position of green flag
(a) (2, 25)
(b) (2, 0.25)
(c) (25, 2)
(d) (0, –25)

Answer: A

Question. Find the position of red flag
(a) (8, 0)
(b) (20, 8)
(c) (8, 20)
(d) (8, 0.2)

Answer: C

Question. What is the distance between both the flags?
(a) √41
(b) √11
(c) √61
(d) √51

Answer: C

Question. 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)

Answer: A

Question. 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) (3.5, 24)
(b) (0.5, 12.5)
(c) (2.25, 8.5)
(d) (25, 20)

Answer: A

Assertion & Reason

DIRECTIONS : Each of these questions contains an Assertion followed by Reason. Read them carefully and answer the question on the basis of following options. You have to select the one that best describes the two statements.
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion : If A(2a, 4a) and B(2a, 6a) are two vertices of an equilateral triangle ABC then, the vertex C is given by (2a + a 3,5a) .
Reason : In equilateral triangle, all the coordinates of three vertices can be rational.
Answer: C

Question. Assertion : The points (k, 2 – 2k), (– k+ 1, 2k) and (– 4 – k, 6 – 2k) are collinear if k = 1/2.
Reason : Three points A, B and C are collinear in same straight line, if AB + BC = AC.
Answer: A

Question. Assertion : Mid-point of a line segment divides line in the ratio 1 : 1.
Reason : If area of triangle is zero that means points are collinear.
Answer: B

Question. Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.
Answer : No

Question. Find a relation between x and y such that the point (x, y) is equidistant from the point(3, 6) and (– 3, 4).
Answer : 3x + y – 5 = 0

Question. Find the point on x-axis which is equidistant from the points (5, −2) and (−3, 2).
Answer : (1, 0).

Question. 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.
Answer : ± 4, QR = √41, PR = 82 , 9 2

Question. If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB.
Answer : (- 2/7, 20/7)

Question. Find the coordinates of the point which divides the join of (–1, 7) and (4, –3) in the ratio 2 : 3.
Answer : (1, 3)

Question. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order.
Answer : 24 sq. units

Question. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4).
Answer : (3, – 10)