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.

Options

A. (0,-5) and (2,0)
B. (0,10) and (-4,0)
C. (0,4) and (-10, 0)
D. (0,-10) and (4,0)

Answer

D

Explanation

Let the coordinates of P and Q (0,y) and (x,0), respectively. So , the mid - point of P (0,y) and Q (x,0) is M `((0+x)/(2),(y+0)/(2))`
[`:.` mid - point of a line segment having points `(x_(1),y_(1))and (x_(2),y_(2)) = ((x_(1)+x_(2))/(2),(y_(1)+x_(2))/(2))]` But it is given that , mid - point of PQ is (2,-5).

`:. 2=(x+0)/(2)`
and `-5=(y+0)/(2)`
`rArr 4=x and -10 =y`
`rArr x=4 and y=-10`
So , the coordinates of P and Q are (0,-10) and (4,0).