Grade 8 Geometry: Similar Figures

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   Point P(6, 4) is dilated by a scale factor of 1.5 with the center of dilation at the origin, to P′. What is the x-coordinate of P′?

   1. A dilation centered at the origin multiplies both coordinates by the scale factor: (x, y) → (1.5x, 1.5y).
   2. P′ = (1.5 × 6, 1.5 × 4) = (9, 6), so the x-coordinate is 9.

   Answer: 9

2. Example 2

   Triangle ABC is similar to triangle DEF. AB = 21 cm, BC = 18 cm, and DE = 7 cm. What is the length of EF, in cm?

   1. In similar triangles, corresponding sides are proportional: AB/DE = BC/EF.
   2. The scale factor from ABC to DEF is 7 ÷ 21 = 0.33 (= 1/3).
   3. EF = 18 × 7 ÷ 21 = 6 cm.

   Answer: 6

3. Example 3

   A rectangle is 6 cm wide and 7 cm long. A similar rectangle is 18 cm wide. How long is the similar rectangle, in cm?

   1. Similar rectangles have proportional sides, so the length grows by the same scale factor as the width.
   2. Scale factor = 18 ÷ 6 = 3.
   3. Length = 7 × 3 = 21 cm.

   Answer: 21