Question

100 Points for this

This series of transformations is performed on a quadrilateral:
a dilation by a factor of 4 with the origin as the center of dilation
a reflection across the y-axis
a 90° counterclockwise rotation about the origin
a translation 3 units down
Arrange the functions representing these transformations in the order in which the transformations occur.
(The tiles are)
f(x, y) = (-4x, 4y)
g(x, y) = (4x, -4y)
h(x, y) = (4x, 4y)
i(x, y) = (4y, 4x − 3)
j(x, y) = (4y, 4x)
k(x, y) = (-4y, -4x)
l(x, y) = (-4y, -4x − 3)

Answer 1

l(x) = (-4y, -4x - 3)

I got the same answer as Mhanifa and if you want the explanation check his, because mine sucks :(

Answer 2

• l(x,y) = (-4y, -4x - 3)

Explanation:

Let's start with function (x, y)

Transformations in the given order result in following

A dilation by a factor of 4 with the origin as the center of dilation

• This results in both coordinates multiplied by 4
• (x, y) → (4x, 4y)

A reflection across the y-axis

• This results in x-coordinate changing sign to opposite
• (4x, 4y) → (-4x, 4y)

A 90° counterclockwise rotation about the origin

• This results in x-coordinate swapping with negative y-coordinate
• (-4x, 4y) → (-4y, -4x)

A translation 3 units down

• This results in y-coordinate change by -3
• (-4y, -4x) → (-4y, 4x - 3)

The final function is:

• l(x) = (-4y, -4x - 3)