# Analytic Geometry Q3

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

Attempt:

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

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

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

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

Finding the value of k:

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

$\displaystyle 4k +13 = 9$

$\displaystyle 4k = 13 - 9$

$\displaystyle 4k = -4$

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

$\displaystyle k = -1$

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

Excellent work!

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

Quote:

$\displaystyle 4k +13 = 9$

$\displaystyle 4k = 13 - 9$

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

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