Question

$M(-2,y)$ is a point equidistant from the coordinates $A(5,7)$ and $B(3,-4)$. Find the value of $y$.

• A.
• B. 2
• C.
• D.

Answer 1

The correct option is A

$M(-2,y)$ is equidistant from $A(5,7)$ and $B(3,-4)$.

​​​​​​$DistanceAM=DistanceBM$
$\sqrt{\left(\right(x_a-x_m{)}^2+(y_a-y_m{)}^2)})$
$=\sqrt{\left(\right(x_b-x_m{)}^2+(y_b-y_m{)}^2)})$

$⟹(5-(-2){)}^2+(7-y{)}^2$
$=(3-(-2){)}^2$ + $(-4-y{)}^2$

$⟹49+49-14y+y^2$
$=25+16+8y+y^2$
$⟹22y=57$
$y=\frac{57}{22}$