Question

in the coordinate plane, the point a(0, 3) is translated to the point a(-1, 4). under the same translation, the points b(-4, 7) and c(-2, 0) are translated to b, and c, respectively. what are the coordinates of b and c?

Explanation:

Step1: Find the translation vector

The original point \( A(0, 3) \) is translated to \( A'(-1, 4) \). The translation vector \( (h, k) \) is found by subtracting the original coordinates from the translated coordinates: \( h = -1 - 0 = -1 \), \( k = 4 - 3 = 1 \). So the translation is \( (x - 1, y + 1) \).

Step2: Translate point \( B(-4, 7) \)

Using the translation vector \( (h, k)=(-1, 1) \), for point \( B(-4, 7) \), the new \( x \)-coordinate is \( -4 + (-1)= -5 \), and the new \( y \)-coordinate is \( 7 + 1 = 8 \). So \( B'(-5, 8) \).

Step3: Translate point \( C(-2, 0) \)

For point \( C(-2, 0) \), the new \( x \)-coordinate is \( -2 + (-1)= -3 \), and the new \( y \)-coordinate is \( 0 + 1 = 1 \). So \( C'(-3, 1) \).

Answer:

\( B'(-5, 8) \), \( C'(-3, 1) \)