Question

practice problems
1 angle abc is taken by a dilation with center p and a scale factor of 3 to angle abc.
the measure of angle abc is 21°. what is the measure of angle abc?
2 here is a diagram with five lines.
select all lines that could be the image of line m by a dilation.
a ℓ
b m
c n
d o
e p

Explanation:

1. For the angle - dilation problem:

Step1: Recall the property of dilation

Dilation is a transformation that changes the size of a figure but not its shape. Angles are preserved under dilation.

Step2: Apply the property to the given angles

Since \( \angle ABC\) is dilated to \( \angle A'B'C'\) and \(m\angle ABC = 21^{\circ}\), by the angle - preservation property of dilation, \(m\angle A'B'C'=m\angle ABC\).

2. For the line - dilation problem:

Step1: Recall the property of line dilation

A dilation of a line \(l\) with a non - zero scale factor \(k\) (where \(k
eq1\)) results in a parallel line if the center of dilation is not on the line. If the center of dilation is on the line, the line maps to itself.

Step2: Analyze each option

• Option A: Line \(l\) is not parallel to line \(m\). So, it cannot be the image of \(m\) under dilation (because dilation of a line (not passing through the center of dilation) gives a parallel line).
• Option B: If the center of dilation is on line \(m\), then \(m\) is its own image (when \(k = 1\), dilation is the identity transformation).
• Option C: Line \(n\) is parallel to line \(m\). So, it can be the image of \(m\) under dilation (if the center of dilation is not on \(m\) and \(n\)).
• Option D: Line \(o\) is not parallel to line \(m\). So, it cannot be the image of \(m\) under dilation.
• Option E: Line \(p\) is parallel to line \(m\). So, it can be the image of \(m\) under dilation (if the center of dilation is not on \(m\) and \(p\)).

Answer:

1. The measure of \( \angle A'B'C'\) is \(21^{\circ}\).
2. B. \(m\), C. \(n\), E. \(p\)