Question

A view of Anytown, USA is shown on the grid below with Rock Park represented by quadrilateral RSTU. Due to overcrowding, another park will be built similar to Rock Park. Vertices A and D are plotted on the grid to represent two corners of new Sandstone ParkWhat could be the ordered pairs representing vertices B and C of quadrilateral ABCD so that Sandstone Park is similar to Rock Park?

Answer 1

Do you have a picture of the grid?

Answer 2

yes

Answer 3

Ahh, that helps a lot. Ok, So what are the vertices of the quadrilateral RSTU?

Answer 4

explain again?????

Answer 5

What are the ordered pairs or coordinates for where the line segments connect in Rock Park (quadrilateral RSTU)?

Answer 6

B(6,6) C(5,5) B(9,3) C(8,2) B(10,4) C(9,3) B(5,4) C(5,3)

Answer 7

SOOO

Answer 8

Patience, grasshopper.
That's not quite right. What is the ordered pair for R?

Answer 9

2,-1?

Answer 10

Almost. It's (3,-1). This grid is a little difficult to read. Remember, the origin is (0,0) so you can count over from there.

Now, how many squares does line segment UR cut through diagonally?
How many squares does the line segment AB cut through?

Answer 11

4?

Answer 12

line segment UR cuts through 2 grid squares diagonally. Are you with me on that?

Answer 13

YES

Answer 14

Ok, great. Now, How many squares does the line segment AB cut through?

Answer 15

OK IM HORRIBLE IN MATH WERES B?SORRY

Answer 16

Oh, sorry. I meant line segment AD. We are trying to find C and D.

How many squares does the line segment AD cut through?

Answer 17

ONE

Answer 18

Ok, great. This is how I though about the problem. If the existing park cuts through two squares diagonally and the new one is going to cut through one square diagonally, what is the size of the new park compared to the existing one?

Answer 19

?

Answer 20

I NEED THE ANSWER PLEEASSSS

Answer 21

I'm not going to give you the answer. I already know how to do the problem and you aren't going to learn anything by me giving you the answer. If you want help solving it, I will help you. Otherwise, good luck!

Answer 22

OK MAN I WANNA LEARN

Answer 23

IS NOT THAT IS THAT IM COMPITING AGAINST TIME IM IN A LITTLE RUSH BUT ILL WAIT

Answer 24

Ok, great. This is how I thought about the problem. If the existing park cuts through two squares diagonally and the new one is going to cut through one square diagonally, what is the size of the new park compared to the existing one?

First, the existing park, Rock Park, cuts through 2 squares diagonally. The new park cuts through 1 square diagonally. So, how much bigger is line segment UR than AD?

Answer 25

is much bigger by one

Answer 26

Yes, good. The line segment is two times bigger. Since the parks are similar, the entire Rock Park is going to be how many times bigger than the new park?

Answer 27

the same?

Answer 28

Yes, twice as big. So now, how long is line segment RS?

Answer 29

is it 4 again?

Answer 30

yes. that means the corresponding segment in the new park is 2, because it is half the size.

Now that you know the size of the new park, you can draw two separate parallelograms from the line segment AD given in the problem. Are you with me on that?

Answer 31

did not get it

Answer 32

Ok, the parallelogram for the new park has 4 sides. The 2 sides parallel to the x-axis are length 2. The other 2 sides cut through one square. So draw a parallelogram incorporating line segment AD as many ways as you can.

There are only two ways to draw a parallelogram from line segment AD. Now are you with me?

Answer 33

yes

Answer 34

OK, so what do you get for the two sets of possibilities for points B and C?

Answer 35

10,4 9,3

Answer 36

Yes, that is one of them. Great Job. The other possibility is on the other side, which would be (6,4) and (5,3).
Good Job.

Answer 37

ufffff thank you so much it was worth it

Answer 38

You're welcome. Geometry can be a really tough class. Good luck!

Answer 39

thnks