richgall____
  • richgall____
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.
Mathematics
jamiebookeater
  • jamiebookeater
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richgall____
  • richgall____
richgall____
  • richgall____
PhantomCrow
  • PhantomCrow
Did you plot the shapes?

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PhantomCrow
  • PhantomCrow
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.
PhantomCrow
  • PhantomCrow
So if you measure the distance between Q and P, then measure the distance between Q' and P'
richgall____
  • richgall____
it didnt give me a graph only thing it gave me was an explanation box to type my answer in
PhantomCrow
  • PhantomCrow
So try graphing it on a piece of paper. A visual really helps.
richgall____
  • richgall____
okay
richgall____
  • richgall____
idk how to find the scale factor
richgall____
  • richgall____
is it when you tell how many units it is moved to the left and right and up and down?
PhantomCrow
  • PhantomCrow
No
PhantomCrow
  • PhantomCrow
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.
PhantomCrow
  • PhantomCrow
Btw, the distance between two points has a formula:\[d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\]
richgall____
  • richgall____
is the scale factor 1/2
PhantomCrow
  • PhantomCrow
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'.
PhantomCrow
  • PhantomCrow
QR AND Q'R', not PQ AND P'Q'. I'm sorry for the typo.
richgall____
  • richgall____
okay
PhantomCrow
  • PhantomCrow
And I go QR=8 AND Q'R'=2 so from there decide the scale factor (how many times larger)

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