MATH SOLVE

5 months ago

Q:
# Which set of transformations has been performed on triangle PQR to form triangle P'Q'R'?A. Dilation by a scale factor of fraction 1 over 2 followed by reflection about the x-axisB. Dilation by a scale factor of 2 followed by reflection about the x-axis C. Dilation by a scale factor of fraction 1 over 2 followed by reflection about the y-axisD. Dilation by a scale factor of 2 followed by reflection about the y-axis

Accepted Solution

A:

Answer: The correct option is(A) Dilation by a scale factor of fraction 1 over 2 followed by reflection about the x-axis.Step-by-step explanation: We are given to select the set of transformations that has been performed on triangle PQR to form triangle P'Q'R'.From the graph, we note thatthe co-ordinates of the vertices of triangle PQR are P(-4, 2), Q(0, 0) and R(2, 6).And, the co-ordinates of the vertices of triangle P'QR' are P'(-2, -1), Q'(0, 0) and R'(1, -3).Let the dilation factor applied on triangle PQR to form triangle P'Q'R' be represented by d.Then, we observe that1/2 × P(-4,2)=(-2,1),1/2 × Q(0,0)=(0,0),1/2 × R(2,6)=(1,3).So, the value of d will bed = 1/2.Again, to arrive at the vertices of triangle P'Q'R', we need to change the sign before the y co-ordinates ((x, y) ⇒ (x, -y)) of each new vertex hat we found after dilation.That is, (-2, 1) ⇒ P'(-2, -1),(0, 0) ⇒ Q'(0, 0),(1, 3) ⇒ R'(1, -3).This is reflection over X-axis.Therefore, the set of transformation is given byDilation by a scale factor of fraction 1 over 2 followed by reflection about the x-axis.Option (A) is CORRECT.