Question

samantha determined that trapezoid (abcdcong abcd). which of the following should be her next step? statement #1: verify that (abcdcong abcd) using the mapping equation for the translation (a(x,y)\to a(x + 8,y)) statement #2: verify that (abcdcong abcd) using the mapping equation for a reflection over the x - axis (a(x,y)\to a(x,-y)) statement #3: verify that (abcdcong abcd) using the mapping equation for a reflection over the y - axis (a(x,y)\to a(-x,y))

Explanation:

Step1: Analyze the transformation

Observe the position of trapezoid $ABCD$ and $A'B'C'D'$. The $x -$ coordinates of the vertices of $ABCD$ increase by 8 to get the vertices of $A'B'C'D'$ while the $y -$ coordinates remain the same. This is a translation.

Step2: Recall transformation rules

The mapping rule for a translation of 8 units to the right is $A(x,y)\to A(x + 8,y)$.

Answer:

Statement #1. Verify that $ABCD\cong A'B'C'D'$ using the mapping equation for the translation $A(x,y)\to A(x + 8,y)$