Answer:
D (-5 , 4) → D' (1 , -4) → D" (-1 , -4) ⇒ 2nd answer
Step-by-step explanation:
* Lets revise some transformation
- If the point (x , y) translated horizontally to the right by h units
∴ Its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
∴ Its image is (x - h , y)
- If the point (x , y) translated vertically up by k units
∴ Its image is (x , y + k)
- If the point (x , y) translated vertically down by k units
∴ Its image is(x , y - k)
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
* Now lets solve the problem
- The point D is (-5 , 4)
- The vector of the translation is <6 , -8>
∵ 6 is positive number
∴ Point D will translate horizontally 6 units to the right
∵ x-coordinate of D = -5
- Add the x-coordinate of D by 6 to find the x-coordinate of D'
∴ The x-coordinate of D' = -5 + 6 = 1
∴ The x-coordinate of D' = 1
∵ -8 is negative number
∴ Point D will translate vertically 8 units down
∵ y-coordinate of D = 4
- Add the y-coordinate of D by -8 to find the y-coordinate of D'
∴ The y-coordinate of D' = 4 + -8 = -4
∴ The y-coordinate of D' = -4
∴ The coordinates of D' are (1 , -4)
- If point (x , y) reflected across the y-axis then its image is (-x , y)
∵ D' is reflected across the y-axis
∵ D' = (1 , -4)
- Change the sign of its x-coordinate
∴ D" = (-1 , -4)
∴ The coordinates of D" are (-1 , -4)
* D (-5 , 4) → D' (1 , -4) → D" (-1 , -4)
