Introduction:

In this problem, we are given a triangle ABC with coordinates A(3,0), B(-2,1), and C(2,1). Our goal is to find the mirror image of this triangle.

Explanation:

To find the mirror image of a triangle, we need to reflect each of its vertices across a mirror line. In this case, let's consider the mirror line to be the x-axis.

Step 1: Plotting the Triangle:

Let's begin by plotting the given triangle ABC using the given coordinates A(3,0), B(-2,1), and C(2,1).

- Point A(3,0): This point lies on the x-axis and is 3 units to the right of the origin.
- Point B(-2,1): This point lies in the second quadrant and is 2 units to the left of the origin and 1 unit above the x-axis.
- Point C(2,1): This point lies in the first quadrant and is 2 units to the right of the origin and 1 unit above the x-axis.

Step 2: Reflecting Point A:

To reflect a point across the x-axis, we need to change the sign of its y-coordinate. The x-coordinate remains the same.

- The mirror image of point A(3,0) will be A'(3,-0) = A'(3,0), as the sign of 0 does not change.
- Therefore, the reflected point A' is still located on the x-axis.

Step 3: Reflecting Point B:

To reflect point B(-2,1) across the x-axis, we need to change the sign of its y-coordinate.

- The mirror image of point B(-2,1) will be B'(-2,-1).
- Therefore, the reflected point B' is located in the fourth quadrant, 2 units to the left of the origin, and 1 unit below the x-axis.

Step 4: Reflecting Point C:

To reflect point C(2,1) across the x-axis, we need to change the sign of its y-coordinate.

- The mirror image of point C(2,1) will be C'(2,-1).
- Therefore, the reflected point C' is located in the third quadrant, 2 units to the right of the origin, and 1 unit below the x-axis.

Step 5: Drawing the Mirror Image Triangle:

Now that we have the reflected points A'(3,0), B'(-2,-1), and C'(2,-1), we can connect them to form the mirror image triangle A'B'C'.

Conclusion:

The mirror image of triangle ABC with coordinates A(3,0), B(-2,1), and C(2,1) is triangle A'B'C' with coordinates A'(3,0), B'(-2,-1), and C'(2,-1).

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