Question

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. (4 points)

Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)

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

Answer 1

The scale factor from triangle PQR to P'Q'R' is 1/4.

The length of each side of the triangle is divided by 4, in other words it is multiplied by the scale factor of 4.

If P'Q'R" is reflected over the y-axis the new points would be: (1, 0) (0, 1) and (-2, 1).

No, the triangles are not congruent. There was a dilation of 1/4 in the triangles.

Answer 2

Answer:

QUESTION 1

Triangles PQR and P'Q'R' has been plotted in the graph.

The green triangle is triangle PQR.

The red triangle is triangle P'Q'R'.

See attachment for graph.

QUESTION 2

Part A

The scale factor can be calculated using the formula,

QUESTION 3

Part B

For a reflection in the y-axis, we negate the x-coordinates. So we negate the x-coordinates of P'Q'R' to obtain the coordinates of P"Q"R".

This implies that,

QUESTION 4

Part C

The two triangles PQR and P′'Q′'R′' are not congruent. The reason is that the two triangles are not equal in all respect. The side lengths are not the same.

If two triangles are congruent, they will have exactly the same three sides and the same three angles.

This means that the two triangles must have the same size and shape. But triangles PQR and P′'Q′'R′' do not have the same size therefore they are not congruent.

Step-by-step explanation: