Question

Copy the graph at the right. On the same set of axes, graph the image of MNOP for a dilation with center (0, 0) and scale factor 2. Use coordinate geometry and the definition of similar polygons to prove that MNOP is similar to its image.

Answer 1

1. P= (1,3), O= (0,0), N= (3,0) M= (3,2) =
P`= (2,6) = (1x2),(3x2)
O`= (0,0) = (0 x 2 = 0), (0 x 2=0)
N`= (6,0) = (1 x 2), (3 x 2)
M`= (6,4) = (3x2), (2x2)

They are similar because all of these corresponds to its sides.
OP corresponds to O P`.
PM corresponds to P' M'.
MN corresponds to M` N`.
ON corresponds to O N`.

You can also know that they are similar because they have the same slope.
OP has the same slopes as O P`.
PM has the same slope P' M'.
MN has the same slope M` N`.
ON has the same slope O N`.

Answer 2

is that correct answer?

Answer 3

The portion where you have

```
P`= (2,6) = (1x2),(3x2)
O`= (0,0) = (0 x 2 = 0), (0 x 2=0)
N`= (6,0) = (1 x 2), (3 x 2)
M`= (6,4) = (3x2), (2x2)
```
is in a strange order. At least to me. I would put the steps first then the final answer after the steps. So maybe say something like

P = (1,3)
P ' = (2*1, 2*3) = (2, 6)

hopefully you see what I mean?

Answer 4

okay is that the correct answer?

Answer 5

one moment

Answer 6

The part where you say
```
You can also know that they are similar because they have the same slope.
OP has the same slopes as O'P`.
PM has the same slope P' M'.
MN has the same slope M' N'.
ON has the same slope O' N'.
```
needs to be proven. You need to find the slopes of each segment and show how you know that slope of OP = slope of O'P', slope of PM = slope of P'M', etc etc

Answer 7

also, you need to compare the ratios of the sides. Other than that, it looks good

Answer 8

what do you mean compare the ratio of the sides

Answer 9

@jim_thompson5910

Answer 10

This is one example

http://gcoopergeometry.weebly.com/uploads/2/0/2/9/20294347/9627618_orig.png

notice how the common ratio (if you divide one side by its corresponding side) is 1/2

Answer 11

okay can i redo and you recheck it

Answer 12

sure

Answer 13

well it doesn't have the sides number as the other one has in the picture

Answer 14

you would use the distance formula to figure out the side lengths

Answer 15

.

Answer 16

@jim_thompson5910

Answer 17

can u check it

Answer 18

it looks much better but you still need to compute the slopes

Answer 19

how do you know that slope of OP = slope of O'P'? show your work on how you found the slopes

Answer 20

Slope Formula

\[\Large m = \frac{y_2 - y_1}{x_2 - x_1}\]

Answer 21

okay thanks

Answer 22

no problem

Answer 23

@jim_thompson5910

Answer 24

very good. I would make sure to simplify all fractions possible. Other than that, it looks perfect

Answer 25

eg: \[\Large \frac{-3}{-1} = 3\]

Answer 26

i have a question the last four dont simlfiy and they dont equal the same number

Answer 27

is that wrong or what?