Question

The figure below represents a DRAFT logo design for an up and coming artist. The logo has been placed on a coordinate grid which represents the front of a t-shirt. Below are the logo’s coordinates A(1,1), B(4,1), and C(4,5). The designer decided they wanted to change the location of the logo on the front of the t-shirt. They said “I will translate the logo five units to the left and two units up followed by the reflection over the line y=0.”

Answer 1

Explanation:

To translate the logo five units to the left and two units up, we need to subtract 5 from the x-coordinates and add 2 to the y-coordinates of each point.

Coordinates after translation:

A: (1-5, 1+2) = (-4, 3)

B: (4-5, 1+2) = (-1, 3)

C: (4-5, 5+2) = (-1, 7)

Next, to reflect the logo over the line y=0, we need to change the sign of the y-coordinates of each point while keeping the x-coordinates the same.

Coordinates after reflection:

A: (-4, -3)

B: (-1, -3)

C: (-1, -7)

Therefore, the new coordinates for the logo after the translation and reflection are:

A: (-4, -3)

B: (-1, -3)

C: (-1, -7)

The logo can now be placed at these new coordinates on the front of the t-shirt.