# Math Help - Analytic Geometry Q1

1. ## Analytic Geometry Q1

Question:
If $(-3,y)$ is equidistant from $(2,6)$ and $(7,-2)$, find $y$.

Attempt:

Distance between two points : $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Distance between $(-3,y)$ and $(2,6)$

$= \sqrt{ (2--3)^2 + (6-y)^2 }$

$= \sqrt{ 25 + 36 - 12y + y^2}$

$= \sqrt{ 61 - 12y + y^2}$

Distance between $(-3,y)$ and $(7,-2)$

$= \sqrt{ (7--3)^2 + (-2-y)^2 }$

$= \sqrt{ 100 + 4 + 4y + y^2 }$

$= \sqrt{ 104 + 4y + y^2 }$

Finding the value of $y$.

$\sqrt{ 61 - 12y + y^2} = \sqrt{ 104 + 4y + y^2 }$

$61 - 12y + y^2 = 104 + 4y + y^2$

$61 - 12y = 104 + 4y$

$61 - 104 = 4y + 12y$

$-43 = 16y$

$y = -\frac{43}{16}$

Is my answer correct?

2. Yes