Question

ABC is dilated by a scale factor of 3 with the origin as the center of dilation, resulting in the image A'B'C'. If the slope of line AB is -1.2, what is the slope of line A'B'?
A. -1.2
B. 3.6
C. 1.2
D 1.8

Answer 1

Answer:

The slope of A'B' = -1.2 ⇒ answer A

Step-by-step explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.  

- It can become larger or smaller, but the shape of the

 figure does not change.  

- The scale factor, measures how much larger or smaller  

  the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- If the center of the dilation is the origin then multiply each coordinate

 by the scale factor

* In the problem

∵ Δ ABC is dilated by a scale factor of 3 with the origin as the center

  of dilation

- Let point A is (a , b) and point B is (c , d)

∵ The slope of the line which passes through points (x1 , y1) and (x2 , y2)

  is m = (y2 - y1)/(x2 - x1)

∴ The slope of AB = (d - b)/(c - a) = -1.2

∵ Point A' is (3a , 3b) and point B' is (3c , 3d)

∴ The slope of A'B' = (3d - 3b)/(3c - 3a)

- Take 3 as a common factor from up and down

∴ The slope of A'B' = 3(d - b)/3(c - a) ⇒ cancel 3 up with 3 down

∴ The slope of A'B' = (d - b)/(c - a) = the slope of AB

∵ The slope of AB = -1.2

∴ The slope of A'B' = -1.2

* The slope of A'B' = -1.2