Answer:
The value of x is 15 ⇒ answer D
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 scale factor is negative then the figure will reflected
* Now lets solve the problem
∵ D (o, k) (x , 9) → (-10 , -6)
- D means dilation
- o means the center of dilation is the origin
- k means the scale factor of dilation
∵ The y-coordinate of the point is 9
∵ The image has y-coordinate -6
∵ The image = The scale factor × the coordinates
∴ -6 = k × 9 ⇒ divide both sides by 9
∴ k = -6/9 = -2/3
- Lets find x by same way
∵ -10 = -2/3 × x ⇒ divide both sides by -2/3
∴ x = -10 ÷ (-2/3) ⇒ change the division to multiplication
∴ x = -10 × (-3/2) = 30/2 = 15
∴ The x-coordinate of the point before dilation is 15
* The value of x is 15
.