2. The pre-image of this point is (-2 , 4)
3. The image of the point is (-3 , -6 , 0)
Step-by-step explanation:
Let us revise the translation of a point
- If the point (x , y) translated horizontally to the right by h units then its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y)
- If the point (x , y) translated vertically up by k units then its image is (x , y + k)
- If the point (x , y) translated vertically down by k units then its image is (x , y - k)
2.
∵ Point (1 , 1) is the image under translation (x , y) → (x + 3 , y - 3)
- That means the point (x , y) is translated 3 units right and
3 units down
∴ x + 3 = 1
- Subtract 3 from both sides
∵ x = -2
∴ y - 3 = 1
- Add 3 to both sides
∴ y = 4
∴ The pre-image of this point is (-2 , 4)
The pre-image of this point is (-2 , 4)
3.
Let us revise the dilation of a point
- If point (x , y) is dilated with center at origin and scale factor k, then its image is (kx , ky)
- If point (x , y , z) is dilated with center origin and scale factor k, then its image is (kx , ky , kz)
∵ Point (-1 , -2 , 0) is dilated with center (0 , 0 , 0) and scale factor 3
- That means multiply each coordinate by 3 to find its image
∴ The image of the point is (3(-1) , 3(-2) , 3(0))
∴ The image of the point is (-3 , -6 , 0)
The image of the point is (-3 , -6 , 0)
Learn more:
You can learn more about dilation in brainly.com/question/2480897
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