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

Question

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

Options:

A . 5722

B . 2

C . 3619

D . 4723

Answer: Option A
:
A

Point M (-2, y) is equidistant from the points A (5, 7) andB(3 , -4).
Distance AM = Distance BM

\Rightarrow \sqrt{((x_{a} - x_{m})^{2} + (y_{a} - y_{m})^{2})})

\sqrt{((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 - 14 y + y^{2} = 25 + 16 + 8 y + y^{2}

\Rightarrow 22 y = 57

\Rightarrow y = \frac{57}{22}

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