# Thread: Analytic Geometry Q1

1. ## Analytic Geometry Q1

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

Attempt:

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

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

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

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

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

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

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

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

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

Finding the value of $\displaystyle y$.

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

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

$\displaystyle 61 - 12y = 104 + 4y$

$\displaystyle 61 - 104 = 4y + 12y$

$\displaystyle -43 = 16y$

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

Is my answer correct?

2. Yes