Question

1. which of the following is the correct algebraic representation for a translation 8 units right and 4 units down?

a. (x + 8, y - 4)
b. (x - 4, y + 8)
c. (x - 8, y + 4)
d. (8x, 4y)

1. which is a true statement about dilations?

a. a dilation sometimes changes the orientation of the vertices.
b. a dilation always preserves congruence.
c. a dilation sometimes enlarges a figure.
d. a dilation always changes the orientation of a figure.

Explanation:

Question 10

Step1: Understand horizontal translation

For a horizontal translation \(h\) units. If \(h>0\), it's to the right. Here \(h = 8\), so \(x\) - coordinate becomes \(x+8\).

Step2: Understand vertical translation

For a vertical translation \(k\) units. If \(k<0\), it's down. Here \(k=-4\), so \(y\) - coordinate becomes \(y - 4\).

• Option A: Dilation does not change the orientation of vertices.
• Option B: Dilation changes the size (so does not preserve congruence). Congruent figures have the same size and shape.
• Option C: If the scale factor \(r>1\), dilation enlarges the figure. If \(0
• Option D: Dilation does not change the orientation of a figure.

Answer:

A. \((x + 8,y-4)\)

Question 11