Question

Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P'Q'R' has vertices P'(4, 0), Q'(3, 1), and R'(−1, −2).
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

Answer:

Part A: The scale factor is 2

Part B:

P''(-4, 0)

Q''(-3, 1)

R''(1, -2)

Part C: No

Step-by-step explanation:

Part A:

The coordinates of the triangle PQR are P(8, 0), Q(6, 2), and R(-2, -4)

The coordinates of the triangle P'Q'R' are P'(4, 0), Q'(3, 1), and R'(-1, -2)

Please find attached the plot of triangles PQR and P'Q'R'

The length of the sides are given by the following formula;

Using an online length

For PQ. the length =

For PR. the length =

For RQ. the length =

While for triangle P'Q'R', we have;

For P'Q'. the length =

For P'R'. the length =

For R'Q'. the length =

∴ PQ = 2 × P'Q'

PR = 2 × P'R'

QR = 2 × Q'R'

Therefore, the scale factor = 2

Part B

By reflecting about the y-axis we have;

Coordinates of the preimage (x, y) after reflection across the y=axis becomes (-x, y)

Therefore, the coordinates of the triangle P''Q''R'' are;

P'(4, 0) after reflection = P''(-4, 0)

Q'(3, 1) after reflection about the y-axis is Q''(-3, 1)

R'(-1, -2) after reflection about the y-axis becomes R''(1, -2)

Part C: No

Given that the triangle P''Q''R'' is congruent to triangle P'Q'R', and triangle P'Q'R' is similar to but not congruent to triangle PQR, we have that triangle P''Q''R'' is similar to but not congruent to triangle PQR.

Step-by-step explanation: