Question

in triangle def, angle d is 100 degrees, angle e is 20 degrees, and angle f is 60 degrees. peter dilates the triangle using a scale factor of 5 to get triangle def. what is the measurement of angle e in triangle def?
○ 20 degrees
○ 100 degrees
○ -30 degrees
○ 70 degrees

what is the rule for reflecting across the y axis? *
your answer

what is the rule for a 180 degree rotation? *
your answer

Explanation:

First Sub - Question (Angle in Dilated Triangle)

Step1: Recall dilation property

Dilation is a transformation that scales the sides of a figure. Angles in a triangle are preserved under dilation.

Step2: Determine angle E'

Since angle E in triangle DEF is 20 degrees and dilation does not change angle measures, angle E in triangle D'E'F' is also 20 degrees.

When reflecting a point \((x,y)\) across the \(y\) - axis, the \(x\) - coordinate changes its sign while the \(y\) - coordinate remains the same. So the rule is \((x,y)\to(-x,y)\).

For a 180 - degree rotation about the origin, a point \((x,y)\) is transformed such that both the \(x\) - coordinate and the \(y\) - coordinate change their signs. The rule is \((x,y)\to(-x,-y)\).

Answer:

A. 20 DEGREES

Second Sub - Question (Reflection across y - axis)