# Thread: Find value of missing co-ordinate

1. ## Find value of missing co-ordinate

Hi,

I'm having trouble with a question, where I need to find the missing co-ordinate.

The question (3:C) is,

I have tried to solve for $k$ by using Pythagoras, but I am still getting the wrong answer, when looking at the answer booklet, and I don't know how to get a second possible answer.

My working is as follows:

If,
$C = (2,-7)$
$E = (5, k)$
$Length = 5$

$(5-2)^2 + (k+7)^2 = 5^2$
$3 + k + 7 = 5$
$k = -5$

According to the answer book, the answers are $-3$ or $-11$.

Again, like all the solution to my questions, I'm sure there's a simple solution to this problem, I'm just missing it.

If anyone can tell me where I'm going wrong with this, and how to find the second possible answer, that would be great.

2. ## Re: Find value of missing co-ordinate

Your method to solve the question is fine, you just have made a mistake by solving the equation.
We have:
$\sqrt{(5-2)^2+(k+7)^2}=5$
$\Leftrightarrow 9+(k+7)^2=25$
$\Leftrightarrow \ldots$

Proceed ...

3. ## Re: Find value of missing co-ordinate

I'm still a bit stumped on solving for $k$ though, as when I square the formula first (following Bodmas), I get:

$3^2 + (k+7)(k+7) = 5^2$
$9 + k^2 + 14k + 49 = 25$

From here, I can square root every term apart from 14k. Where I don't know how to combine the k^2 and the 14k, I'm stuck with either two $k$ terms on one side or one $k$ term on either side of the equation.

4. ## Re: Find value of missing co-ordinate

This is a quadratic equation in $k$:
Originally Posted by ashleysmithd
$9 + k^2 + 14k + 49 = 25$
If you rewrite it as:
$k^2+14k+33=0$
then you can apply the quadratic formula ...

5. ## Re: Find value of missing co-ordinate

Ah.. I tried the quadratic before, but forgot to square $b$ (or $14$) hence getting a negative number, so I assumed using the quadratic formula was wrong.

It's almost always overlooking small details by accident that trips me up.