Question

Can someone help me with this math question it involves transformation

Answer 1

Answer:

ABCD is reflected over the y-axis and translate (x + [-4] , y + [-4])

Step-by-step explanation:

* Lets explain the reflection and the translation

- 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)

- 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)

* Now lets solve the problem

∵ The vertices of ABCD are:

   A = (-5 , 2) , B = (-3 , 4) , C = (-2 , 4) , D = (-1 , 2)

- If ABCD reflected over the y-axis we will change the sign of the

 x-coordinate of all the points

∴ The image of A = (5 , 2)

∴ The image of B = (3 , 4)

∴ The image of C = (2 , 4)

∴ The image of D = (1 , 2)

∴ The image of ABCD after reflection over the y-axis will be at

   the first quadrant  

- The figure EHGF is left and down the image of ABCD after

 the reflection over the y-axis

∴ The image is translate to the left and down

∵ E = (1 , -2) and E is the image of A after reflection and translation

∵ The image of a after reflection is (5 , 2)

- That means 5 became 1 and 2 became -2

∵ 1 - 5 = -4

∴ The image of A after reflection translate 4 units to the left

∵ -2 - 2 = -4

∴ The image of A after reflection translate 4 units down

∴ ABCD is reflected over the y-axis and translate (x + [-4] , y + [-4])

* You can check the rest of points

# B with H

∵ B = (-3 , 4) after reflection over y-axis is (3 , 4) after translation is

   (3 + [-4] , 4 + [-4]) = (-1 , 0) the same with point H = (-1 , 0)

# C with G

∵ C = (-2 , 4) after reflection over y-axis is (2 , 4) after translation is

   (2 + [-4] , 4 + [-4]) = (-2 , 0) the same with point G = (-2 , 0)

# D with F

∵ D = (-1 , 2) after reflection over y-axis is (1 , 2) after translation is

   (1 + [-4] , 2 + [-4]) = (-3 , -2) the same with point F = (-3 , -2)