Question

which choices correctly describe reflections in the diagram? choose three correct answers.
the triangle a is reflected across the x - axis onto triangle b.
the triangle a is reflected across the y - axis onto triangle d.
the triangle d is reflected across the line y = x onto triangle b.
the triangle d is reflected across the x - axis onto triangle c.

Explanation:

Step1: Analyze reflection of triangle A

• For reflection, check the symmetry.
• Triangle A and B: Reflecting triangle A across the line \(y = x\) (swap \(x\) and \(y\) coordinates of vertices).
• Triangle A and D: Reflecting triangle A across the \(y -\)axis (change sign of \(x\) - coordinate of vertices).

Step2: Analyze reflection of triangle D

• Triangle D and C: Reflecting triangle D across the \(x -\)axis (change sign of \(y\) - coordinate of vertices).

Answer:

• The triangle A is reflected across the line \(y=x\) onto triangle B.
• The triangle A is reflected across the \(y -\)axis onto triangle D.
• The triangle D is reflected across the \(x -\)axis onto triangle C.