Question

c. $(2,-4)$
d. $(-4,2)$
what is the result of reflecting a rectangle over the x-axis and then dilating it by a scale factor of 0.75?
a. the size and orientation remain unchanged.
b. the size decreases, and the figure is flipped left to right.
c. the size decreases, and the figure is flipped upside down.
d. the size increases but the orientation remains unchanged.
if a rectangle is translated 5 units left and 3 units down, what will happen to the coordinates of the vertices?
a. the x-coordinates increase by 5, and the y-coordinates decrease by 3.
b. the x-coordinates decrease by 5, and the y-coordinates increase by 3.
c. the x-coordinates increase by 5, and the y-coordinates increase by 3.
d. the x-coordinates decrease by 5, and the y-coordinates decrease by 3.

Explanation:

Step1: Analyze reflection and dilation

A reflection over the x-axis flips the figure upside down (reverses y-coordinates). A dilation with scale factor 0.75 (less than 1) decreases the figure's size.

Step2: Analyze translation coordinates

Translating left subtracts from x-coordinates; translating down subtracts from y-coordinates. 5 units left means x decreases by 5, 3 units down means y decreases by 3.

Answer:

1. c. The size decreases, and the figure is flipped upside down.
2. d. The x-coordinates decrease by 5, and the y-coordinates decrease by 3.