Question

$\overline{pl}$ has endpoints $p(4, -6)$ and $l(-2, 1)$. the segment is translated using the mapping $(x, y) \to (x + 5, y)$. what are the coordinates of $p$ and $l$? $\bigcirc$ $p(9, -6), l(-2, 1)$ $\bigcirc$ $p(4, -6), l(3, 1)$ $\bigcirc$ $p(9, -6), l(3, 1)$ $\bigcirc$ $p(9, -1), l(3, 6)$

Explanation:

Step1: Find \( P' \) coordinates

The mapping is \( (x, y) \to (x + 5, y) \). For point \( P(4, -6) \), substitute \( x = 4 \) and \( y = -6 \) into the mapping. So \( x' = 4 + 5 = 9 \), \( y' = -6 \). Thus, \( P'(9, -6) \).

Step2: Find \( L' \) coordinates

For point \( L(-2, 1) \), substitute \( x = -2 \) and \( y = 1 \) into the mapping. So \( x' = -2 + 5 = 3 \), \( y' = 1 \). Thus, \( L'(3, 1) \).

Answer:

\( P'(9, -6), L'(3, 1) \) (corresponding to the third option: \( P'(9, -6), L'(3, 1) \))