Question

Ben performed a transformation on trapezoid PQRS to create P′Q′R′S′,

As shown in the figure below:
A four-quadrant coordinate grid is drawn:

Trapezoid PQRS with coordinates at P (-6, -3), Q (-4, -3), R (-2, -5), S (-7, -6) and

Trapezoid P prime Q prime R prime S prime with coordinates at
P prime (3, -6), Q prime (3, -4), R prime (5, -2), S prime (6, -7)

What transformation did Ben perform to create P′Q′R′S′?
a. Rotation of 270° counterclockwise about the origin
b. Reflection across the line of symmetry of the figure
c. Reflection across the Y-axis
d. Rotation of 90° counterclockwise about the origin

Answer 1

Answer: A - rotation of 270 degrees counterclockwise about the origin

Explanation:

When a point is rotated 270 degrees counterclockwise, the points change from (x,y) to (-y,x). We can see this when (-4,-3) turns into (-3,4) which we find by doing (-3,-4(-1).

Answer 2

The transformation that Ben performed to create P′Q′R′S′ is a reflection across the Y-axis.

To see this, consider the x-coordinates of the vertices of the original trapezoid PQRS and the transformed trapezoid P′Q′R′S′. The x-coordinates of P and S are negative, while the x-coordinates of Q and R are positive. In the transformed trapezoid, the x-coordinates of P′ and S′ are positive, while the x-coordinates of Q′ and R′ are negative. This suggests that the trapezoid was reflected across the y-axis.

Therefore, the answer is c. Reflection across the Y-axis.