Question

Question 17
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)

Answer 1

Let the coordinate of P and Q (0,y) and (x,0) respectively.
So, the mid-point of P(0,y) and Q(x,0) is
$M(\frac{0+x}{2},\frac{y+0}{2})\left[\begin{array}{c}\because \text{Mid-point of line segment having the points}\\ (x_1,y_1)and(x_2,y_2)\\ =(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\end{array}\right]\text{But it is given, mid-point of PQ is (2, -5)}$
$\therefore 2=\frac{x+0}{2}And-5=\frac{y+0}{2}\Rightarrow 4=xand-10=y\Rightarrow x=4andy=-10\text{So, the coordinates of P and Q are (0,-10) and (4,0).}$