Question

PL has endpoints P(4, −6) and L(−2, 1).

The segment is translated using the mapping (x, y) → (x + 5, y).

What are the coordinates of P’ and L’?
P’(9, -6), L’(-2, 1)
P’(4, -6), L’(3, 1)
P’(9, -6), L’(3, 1)
P’(9, -1), L’(3, 6)

Answer 1

To find the new coordinates of the points P and L after the translation using the mapping \( (x, y) \to (x + 5, y) \), we will add 5 to the x-coordinate of each point and keep the y-coordinate the same.

**For point P(4, -6):**

- New x-coordinate: \( 4 + 5 = 9 \)
- New y-coordinate: \( -6 \)

So, the new coordinates for P' are \( P'(9, -6) \).

**For point L(−2, 1):**

- New x-coordinate: \( -2 + 5 = 3 \)
- New y-coordinate: \( 1 \)

So, the new coordinates for L' are \( L'(3, 1) \).

Putting it together, the coordinates after the translation are:
- \( P'(9, -6) \)
- \( L'(3, 1) \)

Thus, the answer is:

**P’(9, -6), L’(3, 1)**.