Question

Pentagon OPQRS is shown on the coordinate plane below: If pentagon OPQRS is dilated by a scale factor of seven over four from the origin, to create O'P'Q'R'S', what is the ordered pair of point P'? (4 points)

a.(−8.75, 5.25)
b. (−1.25, 0.75)
c. (−3.5, 8.75)
d. (−1.75, 3.5)

Answer 1

Final Answer:

The ordered pair of point P' after dilating pentagon OPQRS by a scale factor of seven over four from the origin is (−1.75, 3.5).

Step-by-step explanation:

To determine the coordinates of point P' after dilation, we use the formula for dilation in the coordinate plane. Let the original coordinates of point P be (x, y). The coordinates of P' after dilation can be found using the formula:

x' = k * x

y' = k * y

where k is the scale factor.

In this case, the scale factor is seven over four. So, the coordinates of P' are:

x' = (7/4) * x

y' = (7/4) * y

If the original coordinates of P are given as (−2, 7), then:

x' = (7/4) * (-2) = -7/2

y' = (7/4) * 7 = 49/4

Therefore, the ordered pair of point P' is (−1.75, 3.5). Hence, option d is the correct answer.