Question

Parallel and Perpendicular Lines: Solve: 7. Given: P(-4,1), Q(2,3), R(4,9), S(-2, 7).
A. Graph quad PQRS.
B. What is the slope of --PQ?(Suppose to be under the line) and of --PS?(Suppose to be under.)
C. What is the slope of --QR?(Suppose to be under.) and of --PS?(Suppose to be under.)
D.Use slopes to show that the diagnoals of quad. PQRS are perpendicular.
E. What kind of quadrilateral is PQRS? Explain.
Show Work (: and Please Help!

Answer 1

Have you graphed it yet?

Answer 2

Yes, I have already graphed it.

Answer 3

Okay, so what is the next step?

Answer 4

There is just really 2 of the parts I don't understand.

Answer 5

I don't understand how to C. and D. After I find the Slope's.

Answer 6

Okay, hold on for a minute

Answer 7

Alright (:

Answer 8

Hmmm, yeah this is interesting. I personally wouldn't prove them to be perpendicular using the method they suggest.

Answer 9

They give you the points, so I would have used the slopes of the diagonals, not the quadrilateral, to prove that their perpendicular to each other.

Answer 10

I'm sorry It was D. & E. I was reading the wrong one lol.

Answer 11

I know that it is a rhombus

Answer 12

But I think it's silly to try to use the slope to prove that the diagonals are perpendicular

Answer 13

I would show it for it to be Perpendicular though?

Answer 14

But actually, the slopes are the same for all four sides so that might be a clue as far as the properties of a rhombus go.

Answer 15

So they are all the same?

Answer 16

Soooo???

Answer 17

Yes, what are the properties of a rhombus? All four sides equal, right?

Answer 18

If all four sides have the same slope, they must be equal in length. It is not possible for a quadrilateral to have four sides with the same slope and the sides not be equal

Answer 19

So, If it would be Perpendicular would you flip the slope and make it negative?

Answer 20

If all four sides of a quadrilateral are equal, by definition, it is a rhombus. Therefore, the diagonals will be perpendicular.

Answer 21

So is that my answer for D.?

Answer 22

Pretty much

Answer 23

Alright Thanks. (:

Answer 24

I admit, it's not a direct proof or anything like that.

Answer 25

You should have asked your instructor what kind of proof he or she wanted

Answer 26

Yeah, I should have. I asked her at the end of the day on Friday and she just said to figure what it would be after you find the slope and perpendicualar.