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

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

Options:

A .

\frac{57}{22}

B . 2

C .

\frac{36}{19}

D .

\frac{47}{23}

Answer: Option A
:
A

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