# Squares, Congruency and Perpendicular bisectors

• Apr 17th 2010, 09:20 AM
(?)G
Squares, Congruency and Perpendicular bisectors
I have a question from my textbook:

Given Square PINK with vertices P (-1,-1), I (3, 2), N (6, -2) and K (2, -5) prove that its diagonals are congruent and are perpendicular bisectors of each other.

I'm really not sure what I am supposed to do once I have this sketched up.
• Apr 17th 2010, 11:24 AM
bjhopper
squares etc
Quote:

Originally Posted by (?)G
I have a question from my textbook:

Given Square PINK with vertices P (-1,-1), I (3, 2), N (6, -2) and K (2, -5) prove that its diagonals are congruent and are perpendicular bisectors of each other.

I'm really not sure what I am supposed to do once I have this sketched up.

Plot the four points. Connect the points Draw the slope diagrams for each side.Prove that each side is equal to 5.Write the slopes for any two lines meeting at one of the points and show that they are perpendicular to each other.You go the rest of the way.

bjh
• Apr 17th 2010, 03:04 PM
Soroban
Hello, (?)G!

Quote:

Given Square PINK with vertices P (-1,-1), I (3, 2), N (6, -2) and K (2, -5)

Prove that its diagonals are congruent and are perpendicular bisectors of each other.

I'm really not sure what I am supposed to do once I have this sketched up.
How about doing the part in blue?

Determine the lengths of diagonals $PN$ and $I\!K$, and show that they are equal.

Find the slopes of $PN$ and $I\!K$ and show they are perpendicular.
Find the intersection of $PN$ and $I\!K$ and show that it is their mutual midpoint.