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

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Solution

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

So, AM = BM

$\sqrt{(x_{a} - x_{m})^{2} + (y_{a} - y_{m})^{2}} = \sqrt{(x_{b} - x_{m})^{2} + (y_{b} - y_{m})^{2}}$

$(x_{a} - x_{m})^{2} + (y_{a} - y_{m})^{2} = (x_{b} - x_{m})^{2} + (y_{b} - y_{m})^{2}$

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

$49 + 49 - 14 y + y^{2} = 25 + 16 + 8 y + y^{2}$

$22 y = 57$

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

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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 $y$ .

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