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:

Analyze the geometric relationship

Using the Geometric Transformations knowledge point
The problem asks to complete the statements regarding quadrilateral \(ABCD\) and quadrilateral \(PQRS\). Since the transformation mapping \(ABCD\) onto \(PQRS\) consists of translations (horizontal and vertical), which are rigid motions, the two quadrilaterals are congruent.

$$ \text{Quadrilateral } ABCD \text{ is congruent to quadrilateral } PQRS. $$

Determine the horizontal translation

Using the Sequence of Transformations knowledge point
Let us find the coordinates of corresponding vertices to determine the translation vector.
Looking at the graph:
Vertex \(A\) is at \((-3, 5)\).
The corresponding vertex \(P\) is at \((1, 1)\).
The horizontal change from \(A\) to \(P\) is:

$$ x_P - x_A = 1 - (-3) = 4 \text{ units} $$

Thus, the horizontal translation is \(4\) units to the right.

Determine the vertical translation

Using the Sequence of Transformations knowledge point
The vertical change from \(A\) to \(P\) is:

$$ y_P - y_A = 1 - 5 = -4 \text{ units} $$

Thus, the vertical translation is \(4\) units down.

Answer:

Quadrilateral \(ABCD\) is <blank>congruent</blank> to quadrilateral \(PQRS\) because a horizontal translation of <blank>4 units to the right</blank> and a vertical translation of <blank>4 units down</blank> maps \(ABCD\) onto \(PQRS\).