Question

Which of the following is true for the points $X$ and $Y$ if the co-ordinates of the mid-points $P$ of $\overline{XY}$ are $(-2,3)$?

• A. $X(-4,-2)$ and $Y(0,4)$
• B. $X(-4,3)$ and $Y(2,2)$
• C. $X(-6,2)$ and $Y(2,4)$
• D. $X(0,2)$ and $Y(-2,4)$

Answer 1

Answer: (C)

Let $X=(x_1,y_1)$ and $Y=(x_2,y_2)$
The co-ordinates of the mid-point $P$ of $\overline{XY}$ is $(-2,3)$.
Now, $P$ is a midpoint of $\overline{XY}$.
$\therefore (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(-2,3)$
$\therefore \frac{x_1+x_2}{2}=-2,\frac{y_1+y_2}{2}=3$
$\therefore x_1+x_2-4,y_1+y_2=6$
For alternate $\left(A\right)$:
$x(-4,-2)$ and $y(0,4)$
$x_1+x_2=-4+0=-4$
$y_1+y_2=-2+4=2$ It is not possible.
For alternate $\left(B\right)$:
$x(-4,3)$ and $y(2,2)$
$x_1+x_2=-4+2=-2$
$y_1+y_2=3+2=5$
It is not possible
For alternate $\left(C\right)$:
$x(-6,2)$ and $y(2,4)$
$x_1+x_2=-6+2=-4$
$y_1+y_2=2+4=6$ It is possible.
$\therefore$ Alternate $\left(C\right)$ is true for the points $X$ and $Y$.