Question

∆PQR was translated and then dilated by a scale factor of 7 to create ∆P''Q''R''. Which statement explains why ∆PQR is similar to ∆P''Q''R''?

Option 1: The angles of ∆PQR are congruent to ∆P''Q''R''.
Option 2: The sides of ∆PQR are proportional to ∆P''Q''R''.
Option 3: ∆PQR has been rotated to form ∆P''Q''R''.
Option 4: Both Options 1 and 2

Answer 1

The reason ΔPQR is similar to ΔP''Q''R'' is because both the angles are congruent and the sides are proportional, due to the translation and dilation by a scale factor of 7.

Step-by-step explanation:

ΔPQR was translated and then dilated by a scale factor of 7 to create ΔP''Q''R''. The statement that explains why ΔPQR is similar to ΔP''Q''R'' is: Both Options 1 and 2. This is because similarity in geometry means that the figures have the same shape but may differ in size.

When a figure is translated (shifted in the plane) and dilated (resized by a scale factor), it retains the same angles, meaning the angles of ΔPQR are congruent to ΔP''Q''R'' (Option 1). Additionally, the corresponding sides are proportional in length, which is the effect of the dilation by the scale factor of 7, making the sides of ΔPQR proportional to ΔP''Q''R'' (Option 2).