Question

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

• A. $\frac{57}{22}$
• B. 2
• C. $\frac{36}{19}$
• D. $\frac{47}{23}$

Answer 1

The correct option is A $\frac{57}{22}$

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

Distance AM = Distance BM
$\Rightarrow \sqrt{\left(\right(x_a-x_m{)}^2+(y_a-y_m{)}^2)})$ = $\sqrt{\left(\right(x_b-x_m{)}^2+(y_b-y_m{)}^2)})$
$\Rightarrow (5-(-2){)}^2$ + $(7-y{)}^2$ = $(3-(-2){)}^2$ + $(-4-y{)}^2$
$\Rightarrow 49+49-14y+y^2=25+16+8y+y^2$
$\Rightarrow 22y=57$
$\Rightarrow y=\frac{57}{22}$