Question

part c

select the correct answer from each drop-down menu.

quadrilateral abcd is choose an answer to quadrilateral pqrs because a horizontal translation of choose an answer and a vertical translation of choose an answer maps abcd onto pqrs.

Explanation:

Identify the geometric relationship

Using the Geometric Transformations knowledge point
Quadrilateral \(ABCD\) is congruent to quadrilateral \(PQRS\) because rigid transformations (translations) preserve side lengths and angle measures.

Determine the horizontal translation

Using the Sequence of Transformations knowledge point
To find the horizontal shift from \(ABCD\) to \(PQRS\), we compare corresponding vertices. Let's find the horizontal change:

$$ \Delta x = x_{PQRS} - x_{ABCD} $$

Looking at the coordinate grid, we determine the horizontal translation is \(6\) units to the right.

Determine the vertical translation

Using the Sequence of Transformations knowledge point
To find the vertical shift from \(ABCD\) to \(PQRS\), we compare corresponding vertices. Let's find the vertical change:

$$ \Delta y = y_{PQRS} - y_{ABCD} $$

Looking at the coordinate grid, we determine the vertical translation is \(5\) units down.

Answer:

Quadrilateral \(ABCD\) is <blank>congruent</blank> to quadrilateral \(PQRS\) because a horizontal translation of <blank>\(6\) units to the right</blank> and a vertical translation of <blank>\(5\) units down</blank> maps \(ABCD\) onto \(PQRS\).