Question

in the coordinate plane, the point a(-3, -2) is translated to the point a(-5, -1). under the same translation, the points b(-1, 1) and c(-5, -5) are translated to b and c, respectively. what are the coordinates of b and c?

Explanation:

Step1: Find the translation vector

To find the translation vector, we subtract the coordinates of point \( A \) from the coordinates of point \( A' \). For the \( x \)-coordinate: \( -5 - (-3) = -5 + 3 = -2 \). For the \( y \)-coordinate: \( -1 - (-2) = -1 + 2 = 1 \). So the translation vector is \( (-2, 1) \), meaning we move 2 units left (subtract 2 from the \( x \)-coordinate) and 1 unit up (add 1 to the \( y \)-coordinate).

Step2: Translate point \( B \)

For point \( B(-1, 1) \), apply the translation. The new \( x \)-coordinate is \( -1 + (-2) = -3 \). The new \( y \)-coordinate is \( 1 + 1 = 2 \). So \( B' \) has coordinates \( (-3, 2) \).

Step3: Translate point \( C \)

For point \( C(-5, -5) \), apply the translation. The new \( x \)-coordinate is \( -5 + (-2) = -7 \). The new \( y \)-coordinate is \( -5 + 1 = -4 \). So \( C' \) has coordinates \( (-7, -4) \).

Answer:

The coordinates of \( B' \) are \( (-3, 2) \) and the coordinates of \( C' \) are \( (-7, -4) \).