Question

d. rotation 180 degrees, then dilation by 1.5

a figure is dilated by a scale factor of -1. what is the result of this transformation?
a. the figure is flipped and moved.
b. the figure remains unchanged.
c. the figure is flipped upside down and resized.
d. the figure is flipped across the origin and maintains its proportions.

a parallelogram is reflected over the line $y = x$. what happens to the coordinates of the point $(4, -2)$?
a. $(4,2)$
b. $(-2,4)$
c. $(2,-4)$
d. $(-4,2)$

what is the result of reflecting a rectangle over the x-axis and then dilating

Explanation:

Step1: Analyze dilation by -1

A scale factor of -1 means the figure is reflected across the origin (since the negative sign flips both x and y coordinates) and the size stays the same (since the absolute value of the scale factor is 1, so proportions are maintained).

Step2: Analyze reflection over y=x

The rule for reflecting a point $(x,y)$ over the line $y=x$ is to swap the x and y coordinates, so $(x,y) \to (y,x)$.

Answer:

1. d. The figure is flipped across the origin and maintains its proportions.
2. b. $(-2,4)$