SOLUTION: A quadrilateral ABCD is formed by the points A(-3,2),B(4,3),C(9,-2) and D(2,-3) (a)show that all four sides are equal in length (b)show that ABCD is not a square

Question 1162029: A quadrilateral ABCD is formed by the points A(-3,2),B(4,3),C(9,-2) and D(2,-3)
(a)show that all four sides are equal in length
(b)show that ABCD is not a square
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A quadrilateral ABCD is formed by the points
A(-3,2),B(4,3),C(9,-2) and D(2,-3)
(a)show that all four sides are equal in length
---------------
It's important the the points are in order around the figure.
---
Find the 4 lengths.
For AB: d^2 = diffy^2 + diffx^2 = (-3-4)^2 + (2-3)^2
Finding d^2 is sufficient, taking the sq root is not necessary.
Do the same for BC, CD and DA.
===============================

(b)show that ABCD is not a square
2 ways to do this:
Find the slopes of AB, BC, CD and DA
Iff adjacent sides are perpendicular, it's a square.
o/w not.
PS Iff = if and only if
==================
Find the distances AC and BD.
IFF they're equal, it's a rectangle, and if the sides are equal it's a square.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Use the distance formula to find the measure of each of the four line segments that form the quadrilateral. If you get the same answer all four times, the line segments are all of equal measure.

Distance formula:

Use the slope formula to calculate the slope of the lines containing the four line segments. If the quadrilateral is square, two of the lines will have slopes equal to each other, and the other two lines will also have equal slopes and these two slopes will be the negative reciprocal of the other two. If this is not true, the quadrilateral is not a square.

Slope formula:

John

My calculator said it, I believe it, that settles it

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