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

Question 20
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)
Let co-ordinates of P be (0, y)
Let co-ordinates of Q be (x, 0)
Since A (2, −5) is mid-point of PQ
(2,−5)=((0 + 𝑥)/2,(𝑦 + 0)/2)
(2,−5)=(𝑥/2,𝑦/2)
Comparing x and y coordinates
2 = 𝑥/2
2 × 2 = x
x = 4
−5 = 𝑦/2
−5 × 2 = y
y = −10
Thus,
Coordinates of P = (0, y) = (0, −10)
Coordinates of Q = (x, 0) = (4, 0)
So, the correct answer is (D)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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