Question

M (c, -1) is a point equidistant from the points A(1, 3) and B(-5, -5). Find the value of c.

• A. 2
• B. -2
• C. 4
• D. 0

Answer 1

The correct option is B

-2

Given

$\because$ Distance between points $(x_1,y_1)$ and$(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.

$\therefore$ AM = $\sqrt{(c-1{)}^2+(-1-3{)}^2}$ and BM = $\sqrt{(c-(-5\left){)}^2\right(-1-(-5){)}^2}$

$\because$ Distance AM = Distance BM
$\therefore \sqrt{(c-1{)}^2+(-1-3{)}^2}=\sqrt{(c-(-5\left){)}^2\right(-1-(-5){)}^2}\Rightarrow \sqrt{(c-1{)}^2+16}=\sqrt{(c+5{)}^2+16}\Rightarrow (c-1{)}^2+16=(c+5{)}^2+16\Rightarrow -2c+17=10c+41\Rightarrow 12c=-24\Rightarrow c=-2$

$\therefore$ Point M is $(-2,-1)$.