Question

fill in the blanks 10 points
given △abc with points a(-2, 3), b(1, 0), and c(-3, 1), graph it, and its image when transformed 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), gráficarlo, y su imagen cuando se transforme 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; reflección sobre y = x;
2nd: < -3, 2 >;
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 \( A(-2, 3) \), \( A' = (3, -2) \)
• For \( B(1, 0) \), \( B' = (0, 1) \)
• For \( C(-3, 1) \), \( C' = (1, -3) \)

Step2: Translate by \( \langle -3, 2

angle \)
To translate a point \((x, y)\) by \( \langle h, k
angle \), we use the rule \( (x + h, y + k) \). Here, \( h = -3 \) and \( k = 2 \).

• For \( A'(3, -2) \), \( A'' = (3 - 3, -2 + 2) = (0, 0) \)
• For \( B'(0, 1) \), \( B'' = (0 - 3, 1 + 2) = (-3, 3) \)
• For \( C'(1, -3) \), \( C'' = (1 - 3, -3 + 2) = (-2, -1) \)

Answer:

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