# Thread: Finding the Perpendicular bisector.

1. ## Finding the Perpendicular bisector.

I have another one of those questions I'd like to double check.

Question:
What is the perpendicular bisector of the line between points (2,2) and (6,6)?

Working:
slope= $\frac{6-2}{6-2}=\frac{4}{4}=1$
Since a perpendicular bisector has a reciprocal slope to the line it bisects, the slope of the bisector is $-\frac{4}{4}=-1$
The midpoint of the bisected line is (4,4) as shown by the midpoint formula: $\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}$ where $x_1=2$, $x_2=6$, $y_1=2$ and $y_2=6$. I'll use the point-slope formula to find the line, so:
let, $y_1=4$, $x_1=4$, and slope=-1, $y-y_1=slope(x-x_1)\rightarrow y-4=-1(x-4)\rightarrow y-4=-x+4 \rightarrow -x-y=8$.

The equation of the bisecting line is: $-x-y=8$

Is my working and answer correct?

2. Originally Posted by MathBlaster47
I have another one of those questions I'd like to double check.

Question:
What is the perpendicular bisector of the line between points (2,2) and (6,6)?

Working:
slope= $\frac{2+6}{2},\frac{2+6}{2}=\frac{4}{4}=1$
Since a perpendicular bisector has a reciprocal slope to the line it bisects, the slope of the bisector is $-\frac{4}{4}=-1$
The midpoint of the bisected line is (4,4) as shown by the midpoint formula: $\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}$ where $x_1=2$, $x_2=6$, $y_1=2$ and $y_2=6$. I'll use the point-slope formula to find the line, so:
let, $y_1=4$, $x_1=4$, and slope=-1, $y-y_1=slope(x-x_1)\rightarrow y-4=-1(x-4)\rightarrow y-4=-x+4 \rightarrow -x-y=8$.

The equation of the bisecting line is: $-x-y=8$

Is my working and answer correct?

Hey MathBlaster47! Really good job so far. You did everything perfectly except for the very last step. The correct answer:

$y-4=-x+4 \rightarrow -x-y=-8 \rightarrow x+y=8$

You did everything else very well, well done on the presentation!

3. Thanks!
So I forgot to place the "-" signs where they were needed, effectively skipping a step.
I see why I was incorrect though, as -4+4 doesn't equal 8--it equals 0!

I have to present math working like that because it is the only way I understand what I'm saying!

4. Originally Posted by MathBlaster47
Thanks!
So I forgot to place the "-" signs where they were needed, effectively skipping a step.
I see why I was incorrect though, as -4+4 doesn't equal 8--it equals 0!

I have to present math working like that because it is the only way I understand what I'm saying!
You're very welcome.

And your presentation makes it easy for me to follow you and find out exactly where you went wrong.