Question

which explanation for the congruency of the trapezoids is correct? statement #1: the trapezoids are congruent because abcd was reflected over the line y = x. statement #2: the trapezoids are congruent because abcd was translated left 4 units and up 2 units. statement #3: the trapezoids are congruent because abcd was rotated 270° (counterclockwise). statement #4: the trapezoids are congruent because abcd was rotated 90° (counterclockwise). (1 point) statement = is correct.

Explanation:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(-y,x)$.

Step2: Check vertices

Let's assume a vertex of trapezoid $ABCD$ say $A(2,1)$. After a 90 - degree counter - clockwise rotation about the origin, using the rule $(-y,x)$, we get $A'(-1,2)$. Similarly, for other vertices of $ABCD$ and their corresponding vertices in $A'B'C'D'$, the 90 - degree counter - clockwise rotation rule holds.

Step3: Analyze other statements

For reflection over $y = x$, the rule is $(x,y)\to(y,x)$. For translation left 4 units and up 2 units, the rule is $(x,y)\to(x - 4,y + 2)$. For 270 - degree counter - clockwise rotation, the rule for a point $(x,y)$ is $(y,-x)$. These do not match the transformation from $ABCD$ to $A'B'C'D'$.

Answer:

Statement #4