Grade 8 Geometry: Transformations

Worked examples

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

1. Example 1

   Point P(−6, −5) is reflected across the y-axis to P′. What is the x-coordinate of P′?

   1. Reflecting across the y-axis keeps y the same and changes the sign of x: (x, y) → (−x, y).
   2. P′ = (6, −5), so the x-coordinate is 6.

   Answer: 6

2. Example 2

   A translation moves point A(7, −4) to A′(12, 1). How many units right does the point move?

   1. Compare the x-coordinates: 7 → 12.
   2. The change is 12 − 7 = 5, so the point moves 5 units right.

   Answer: 5 units

3. Example 3

   Point P(−4, 3) is translated 6 units right and 1 unit up to P′. What is the y-coordinate of P′?

   1. A translation adds the same amount to every point: (x, y) → (x + 6, y + 1).
   2. P′ = (−4 + 6, 3 + 1) = (2, 4), so the y-coordinate is 4.

   Answer: 4