Question

Medal!
Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, –4), and R(–8, –4). Triangle P'Q'R' has vertices P'(1, 0), Q'(0, –1), and R'(–2, –1).

Plot triangles PQR and P'Q'R' on your own coordinate grid.

Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R'? Explain your answer.

Part B: Write the coordinates of triangle P"Q"R" obtained after P'Q'R' is reflected about the y-axis.

Part C: Are the two triangles PQR and P''Q''R'' congruent? Explain your answer.

Answer 1

@PhantomCrow

Answer 2

@amarimiller @Joehoffy

Answer 3

Did you plot the shapes?

Answer 4

When you plot the graphs, use the distance formula to measure the distance between two points on the original triangle, and then find the distance of the scaled triangle, using the prime of the same points.

Answer 5

So if you measure the distance between Q and P, then measure the distance between Q' and P'

Answer 6

it didnt give me a graph only thing it gave me was an explanation box to type my answer in

Answer 7

So try graphing it on a piece of paper. A visual really helps.

Answer 8

okay

Answer 9

idk how to find the scale factor

Answer 10

is it when you tell how many units it is moved to the left and right and up and down?

Answer 11

No

Answer 12

Okay. That's fine. The scale factor is simply how much larger the shape is than its translation. Graphing it shows you that it is smaller, but it doesn't tell you by what factor. If we find the distance between two points (or a side of the triangle) in the original one, then we can find the distance of the proportional length in the scaled triangle and whatever factor the large length is bigger compared to the smaller one, is your scale factor.

Answer 13

Btw, the distance between two points has a formula:\[d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\]

Answer 14

is the scale factor 1/2

Answer 15

I have to go soon, so find the distance using that formula between Q and R and then on the other triangle, find the distance between Q' and R'. Then, compare how many times larger PQ is than P'Q'.

Answer 16

QR AND Q'R', not PQ AND P'Q'. I'm sorry for the typo.

Answer 17

okay

Answer 18

And I go QR=8 AND Q'R'=2 so from there decide the scale factor (how many times larger)