Question

a parallelogram is reflected over the line y = x. what happens to the coordinates of the point (4, -2)?
a. (2, -4)
b. (4, 2)
c. (-4, 2)
d. (-2, 4)
how does applying a dilation with a scale factor of 1.5 affect a triangle’s area?

Explanation:

Step1: Recall reflection rule

For a reflection over the line $y = x$, the rule is $(x,y)\to(y,x)$.

Step2: Apply rule to point

Given the point $(4,-2)$, applying the rule $(x,y)\to(y,x)$ gives $(-2,4)$.

Step3: Recall dilation - area relationship

If the scale - factor of a dilation is $k$, the ratio of the areas of the dilated figure to the original figure is $k^{2}$.

Step4: Calculate new area factor

Given $k = 1.5$, then $k^{2}=(1.5)^{2}=2.25$. So the area of the triangle is multiplied by 2.25.

Answer:

1. D. (-2, 4)
2. The area of the triangle is multiplied by 2.25.