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. None of these

Answer 1

The correct option is D None of these

Distance AM = Distance BM
$\Rightarrow \sqrt{(c-1{)}^2+(1-3{)}^2}=\sqrt{(c-(-5\left){)}^2\right(1-(-5){)}^2}\Rightarrow \sqrt{(c-1{)}^2+4}=\sqrt{(c+5{)}^2+36}\Rightarrow (c-1{)}^2+4=(c+5{)}^2+36\Rightarrow -2c+5=10c+61\Rightarrow 12c=-56\Rightarrow c=-4.67$

The point equidistant from A and B is $(-4.67,1)$.