MATH SOLVE

3 months ago

Q:
# Can someone help me with this math question it involves transformation

Accepted Solution

A:

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)