# Thread: Show the right bisectors of eachother.

1. ## Show the right bisectors of eachother.

There's nothing i'm more confused with then bisectors.

The points are, P(3,2) - S(5,8) - R(11,10) and Q (9,4).

The question is, Show that the diagonals of PQRS are the right bisectors of eachother. Use midpoints and slopes in your solution.
So i'm assuming you get the midpoint of each, then the slopes of S and Q. Then the slopes of P and Q.

Then they should be perpendicular to eachother? Which makes them the right bisectors of eachother?
I don't fully understand the question. Not sure if my theory is right or not, anyway.

Thanks

2. Originally Posted by rocky123
The points are, P(3,2) - S(5,8) - R(11,10) and Q (9,4).
PR: slope = (10-2)/(11-3) = 1
QS: slope = (8-4)/(5-9) = -1
So they cross at right angles; carry on...

3. Originally Posted by Wilmer
PR: slope = (10-2)/(11-3) = 1
QS: slope = (8-4)/(5-9) = -1
So they cross at right angles; carry on...

Yeah, but is that my answer?
Because I see no use of midpoints.

I'm just a bit confused, because "Show that they are the right bisectors of eachother" which would cause them to be perpendicular.

So therefore what you did tell me is the right answer, yet there's no use of midpoints?

4. Originally Posted by rocky123
The points are, P(3,2) - S(5,8) - R(11,10) and Q (9,4).
The question is: Show that the diagonals of PQRS are the right bisectors of each other. Use midpoints and slopes in your solution.
Question would be clearer this way:
Show that the diagonals PR and QS cross at right angles,
and bisect each other.

We've shown that they cross at right angles, from slopes being 1 and -1.

So now to show that that bisect each other:
midpoint of PR = (7,6)
midpoint of QS = (7,6)
So they bisect each other!
I'm sure you know how to get the 2 midpoints

5. ... /facepalm.

I see now, I just wrote down the midpoints and then used the slope formula on the midpoints.

Time to throw that in the garbage... Ugh.