Question

quadrilaterals pqrs, i, ii, iii, and iv are shown on the coordinate grid below.

which quadrilateral is similar to pqrs because of a dilation with a scale factor of 2?
i
ii
iii
iv

Explanation:

Step1: Identify PQRS side lengths

First, count grid units for PQRS sides:

• Vertical side: $3$ units
• Horizontal side: $4$ units

Step2: Calculate scaled side lengths

Apply scale factor $2$:

• Scaled vertical side: $3 \times 2 = 6$ units
• Scaled horizontal side: $4 \times 2 = 8$ units

Step3: Match to quadrilaterals

Check each option:

• I: Smaller than PQRS (scale factor <1)
• II: Sides are $6$ and $8$ units (matches scaled lengths)
• III: Same size as PQRS (scale factor=1)
• IV: Larger but not 2x scale

Answer:

II