Question

Please help. Will fan and medal!
A quadrilateral has vertices at A(-5, 5), B(1, 8), C(4, 2), and D(-2, -2). Use slope to determine if the quadrilateral is a rectangle. Show your work.

Answer 1

@myininaya

Answer 2

@ganeshie8

Answer 3

@amistre64

Answer 4

well find the slope of AB

then BC and show that they are perpendicular... so the product of the slopes is -1.

then find the slope of CD and DA... and you'll see some slopes which are identical to AB and BC... so the opposite sides are parallel.

hope it helps

Answer 5

could you work through it with me? @campbell_st

Answer 6

ok... so do you know the formula for the slope of a line..?

Answer 7

errr... no.

Answer 8

m = [y1 - y2] / [x1 - x2].??

Answer 9

slope is 1/2?

Answer 10

ok... well that makes it hard.

Here is the slope formula you would find in any textbook.

m is the slope

\[m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\]

so let A( -5, 5) be the 1 points and B(1, 8) be the 2 points

so you substitute into the equation

\[m = \frac{8 - 5}{1 - -5} = \frac{3}{6}... or..... \frac{1}{2}\]

so the slope of AB is 1/2

now do BC

let B(1, 8) be the 1 point and C (4, 2) be the 2 point...

can you find the slope of BC

Answer 11

-2?

Answer 12

Now do I do CD?

Answer 13

@campbell_st

Answer 14

ok... great.... to prove they lines are AB and BC are perpendicular multiply the 2 slopes and you should get -1... if so... the lines meet at right angles.

Does that make sense...

Answer 15

So it is indeed a rectangle?

Answer 16

then find CD... and it should have the same slope as AB... which means it's parallel to AB...

find the slope of DA and it should be the same as BC

then you have shown sides are parallel and meet at right angles... properties of a rectangle... well done