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
