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 A (5, 7) and B(3 , -4)

Distance AM = Distance BM

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