Answer:
The image of point (x , y) by dilation with center origin and scale factor k is (kx , ky)
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
* In a problem of dilation
∵ The center of dilation is the origin
∵ The scale factor of dilation is k
∵ The point is (x , y)
- In dilation with center origin and scale factor k to find the image
of the point multiply each coordinates of the point by the scale
factor k because the distance d between the point and the
origin will be equal kd which is the distance between the origin
and the image of the point d is depending on the coordinates
of the point
∴ The image of point (x , y) by dilation with center origin and
scale factor k is (kx , ky)
* Ex: If point A is (3 , 4)
∵ The distance from the origin to point A = [tex]\sqrt{(3)^{2}+(4)^{2}}=\sqrt{9+16}=\sqrt{25}=5[/tex]
∵ The scale factor of dilation is 2 and the center is the origin
∴ The image of A is A' = (3 × 2 , 4 × 2) = (6 , 8)
∵ The distance from the origin to point A' = [tex]\sqrt{(6)^{2}+(8)^{2}}=\sqrt{36+64}=\sqrt{100}=10[/tex]
∵ 10 ÷ 5 = 2 which is the value of the scale factor
∴ The image of point (x , y) by dilation with center origin and
scale factor k is (kx , ky)
