Question

Graph AABC with vertices A(0, 2), B(3, 2), and C(2, 1) and its image after a reflection in the x-axis.

Answer 1

To graph the triangle AABC, we can plot the coordinates of the three vertices and then connect them to form the triangle. The coordinates of the vertices are (0, 2), (3, 2), and (2, 1), so we can plot these points on a coordinate grid and connect them with line segments to form the triangle:

|

|

| (2,1)

| /

| /

| /

|/

(0,2) __________ (3,2)

To reflect the triangle in the x-axis, we can multiply the y-coordinate of each vertex by -1. This will cause the triangle to be flipped over the x-axis. The coordinates of the reflected triangle are (0, -2), (3, -2), and (2, -1), so we can plot these points on the same coordinate grid and connect them with line segments to form the reflected triangle:

|

|

|

| /\

| / \

| / \

|/ \

(0,2) __________ (3,2)

|

|

| (2,-1)

|

The resulting graph shows the original triangle AABC and its image after reflection in the x-axis.

Answer 2

A' = (0, -2)

B' = (3, -2)

C' = (2, -1)

Explanation:

Given vertices of triangle ABC:

• A = (0, 2)
• B = (3, 2)
• C = (2, 1)

The mapping rule for a reflection in the x-axis is:

• (x, y) → (x, -y)

Therefore, the vertices of ΔA'B'C' are:

• A' = (0, -2)
• B' = (3, -2)
• C' = (2, -1)