Question

given △abc with points a(-2, 3), b(1, 0), and c(-3, 1), graph it, and its image when translated as indicated. then fill in the points for △abc in the space provided after the first transformation. then fill in the points for △abc in the space provided after the second transformation.
dado △abc con los puntos a(-2, 3), b(1, 0) y c(-3, 1), graficarlo, y su imagen cuando se traduce como se indica. a continuación, rellene los puntos de △abc en el espacio proporcionado después de la primera transformación. a continuación, rellene los puntos de △abc en el espacio proporcionado después de la segunda transformación.
1st: reflection over y = x, refleción sobre y = x;
2nd: x - 2, 4s?
answer:
a ( type your answer... , type your answer... )
b ( type your answer... , type your answer... )
c ( type your answer... , type your answer... )
a ( type your answer... , type your answer... )
b ( type your answer... , type your answer... )
c ( type your answer... , type your answer... )

Explanation:

Step1: Reflect over \( y = x \)

To reflect a point \((x, y)\) over the line \( y = x \), we swap the \( x \)- and \( y \)-coordinates. So for each point:

• For \( A(-2, 3) \), the reflection \( A' \) is \( (3, -2) \).
• For \( B(1, 0) \), the reflection \( B' \) is \( (0, 1) \).
• For \( C(-3, 1) \), the reflection \( C' \) is \( (1, -3) \).

Step2: Translate by \( \langle -2, 4

angle \)
To translate a point \((x, y)\) by the vector \( \langle h, k
angle \), we use the rule \( (x + h, y + k) \). Here, \( h = -2 \) and \( k = 4 \).

• For \( A'(3, -2) \), the translation \( A'' \) is \( (3 + (-2), -2 + 4) = (1, 2) \).
• For \( B'(0, 1) \), the translation \( B'' \) is \( (0 + (-2), 1 + 4) = (-2, 5) \).
• For \( C'(1, -3) \), the translation \( C'' \) is \( (1 + (-2), -3 + 4) = (-1, 1) \).

Answer:

• \( A' \): \( (3, -2) \)
• \( B' \): \( (0, 1) \)
• \( C' \): \( (1, -3) \)
• \( A'' \): \( (1, 2) \)
• \( B'' \): \( (-2, 5) \)
• \( C'' \): \( (-1, 1) \)