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

Answer 1

The correct option is B -2

Given that point M is equidistant from points A(1, 3) and B(-5, -5).
$\Rightarrow$ AM = BM

Distance between two points $(x_1,y_1)\text{and}(x_2,y_2)=(\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

AM = BM
$\Rightarrow \sqrt{(c-1{)}^2+(-1-3{)}^2}=\sqrt{(c-(-5){)}^2+(-1-(-5){)}^2}$
$\Rightarrow \sqrt{(c-1{)}^2+16}=\sqrt{(c+5{)}^2+16}\Rightarrow (c-1{)}^2+16=(c+5{)}^2+16\Rightarrow (c-1{)}^2=(c+5{)}^2\Rightarrow c^2+1-2c=c^2+25+10c\Rightarrow 12c=-24\Rightarrow c=-2$

$\therefore$ The value of c is -2.