# Analytic Geometry Q3

• January 30th 2009, 07:46 AM
looi76
Analytic Geometry Q3
Question:
Find the value of $k$ if $(0,2)$ is equidistant from the points $(3,k)$ and $(k,5)$.

Attempt:

Distance between points $(0,2)$ and $(3,k)$:

$= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
$= \sqrt{(3-0)^2+(k-2)^2}$
$= \sqrt{9+k^2-4k+4}$
$= \sqrt{k^2+4k+13}$

Distance between points $(0,2)$ and $(k,5)$:

$= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
$= \sqrt{(k-0)^2+(5-2)^2}$
$= \sqrt{k^2+9}$

Finding the value of k:

$\sqrt{k^2+4k+13} = \sqrt{k^2+9}$

$4k +13 = 9$

$4k = 13 - 9$

$4k = -4$

$k = \frac{-4}{4}$

$k = -1$

• January 30th 2009, 08:13 AM
Soroban
Hello, looi76!

Excellent work!

Just a silly error near the end . . . the slap-head type . . .

Quote:

$4k +13 = 9$

$4k = 13 - 9$

$4k = {\color{red}-}4$

Of course, $13-9 \:=\:{\color{red}+}4$