Question

Quadrilateral pqrs, with the vertex p(-5,-3), undergoes a transformation to form quadrilateral P’Q’R’S’, with p’ at (5,3). The type of transformation pqrs undergoes is a ____ . If vertex Q is at (-4,-5), then vertex Q’ is at ____.

A) translation, Q’(-4,-5)
B) reflection, Q’(4,5)
C) rotation, Q’(4,5)
D) dilation, Q’(-8,-10)

Answer 1

The transformation is a reflection, changing the sign of both coordinates. If vertex Q is at (-4,-5), then after the reflection, vertex Q' is at (4,5).

Step-by-step explanation:

The transformation that quadrilateral PQRS undergoes to form quadrilateral P'Q'R'S' is a reflection, as we can tell from the original and transformed coordinates of vertex P and P'. In a reflection over the x- and y-axes, if point P(-5,-3) is reflected to P'(5,3), then each coordinate is reflected to its opposite; that is, -5 reflects to 5, and -3 reflects to 3.

Following this pattern, if vertex Q is at (-4,-5), then vertex Q' will also reflect over the x- and y-axes to become (4,5). This demonstrates that both x and y coordinates have their signs changed from negative to positive.

Therefore, the correct answer is B) reflection, Q'(4,5). The type of transformation PQRS undergoes is a reflection, and if vertex Q is at (-4,-5), then vertex Q' is at (4,5).