Question

trapezoid abcd and its transformation are shown on the coordinate grid. which sequence of transformations could correctly map trapezoid abcd to its image? select two correct answers. a. reflect over the y - axis, translate 1 unit left and one unit down. b. reflect over the y - axis, translate 1 unit right and one unit down c. translate 5 units right and one unit down d. translate 1 unit right and one unit down, reflect over the y - axis e. rotate 90° clockwise, translate 1 unit down.

Explanation:

Step1: Analyze reflection over y - axis

When a point $(x,y)$ is reflected over the $y$-axis, it becomes $(-x,y)$.

Step2: Analyze translation

Translation of a point $(x,y)$ by $a$ units right and $b$ units down gives $(x + a,y - b)$.
Let's assume a vertex of trapezoid $ABCD$, say $A(-7,-3)$.
If we first reflect $A$ over the $y$-axis, we get $A'(7,-3)$. Then if we translate $1$ unit right and $1$ unit down, we get $A''(7 + 1,-3-1)=(8,-4)$.
If we first translate $A(-7,-3)$ $1$ unit right and $1$ unit down, we get $A_1(-7 + 1,-3-1)=(-6,-4)$. Then reflecting over the $y$-axis gives $A_2(6,-4)$.
For a translation of $5$ units right and $1$ unit down, starting with $A(-7,-3)$, we get $A'(-7+5,-3 - 1)=(-2,-4)$.

Step3: Check option B

If we reflect a point of trapezoid $ABCD$ over the $y$-axis and then translate 1 unit right and 1 unit down, it matches the transformation of the trapezoid.

Step4: Check option D

If we first translate a point of trapezoid $ABCD$ 1 unit right and 1 unit down and then reflect over the $y$-axis, it also matches the transformation of the trapezoid.

Answer:

B. Reflect over the y - axis, translate 1 unit right and one unit down
D. Translate 1 unit right and one unit down, reflect over the y - axis