Question

In the dilated isosceles right triangle ABC, where line segment AB has a slope of -1 and ∠ABC = 90°, ABC is dilated by a scale factor of 1.8 with the origin as the center of dilation, resulting in the image A'B'C'. What is the slope of line segment B'C'?

a. -1
b. 0
c. 1
d. 1.5
e. 2

Answer 1

The slope of line segment B'C' after dilation is -1 because dilation changes size but not the slope or shape of the geometric figure.

Step-by-step explanation:

The question involves understanding the properties of dilation in geometry and the concept of slope. We are given that triangle ABC is an isosceles right triangle with a slope of -1 for line segment AB, and angle ABC is 90 degrees. Upon dilation by a scale factor of 1.8 with the origin as the center of dilation, we obtain the dilated triangle A'B'C'. It's important to note that dilation affects the size but not the shape of a geometric figure, so angles and slopes of the corresponding sides remain unchanged.

Therefore, since the slope of AB is -1 before dilation, the slope of the dilated segment B'C' will also be -1. The correct answer to the question "What is the slope of line segment B'C'?" is: a. -1.