To graph triangle $A'B'C'$ after applying the transformation $(x, y) \rightarrow (x, -y)$, follow these steps:

Step 1: Identify the coordinates of points A, B, and C.

Let's assume the coordinates of $A$, $B$, and $C$ are given. If not, you can either measure or be provided with the coordinates on the coordinate plane.

• Let $A(x_1, y_1)$, $B(x_2, y_2)$, and $C(x_3, y_3)$.

Step 2: Apply the transformation $(x, y) \rightarrow (x, -y)$.

This transformation reflects each point across the x-axis, meaning that only the y-coordinate changes its sign while the x-coordinate remains the same.

• $A'(x_1, -y_1)$
• $B'(x_2, -y_2)$
• $C'(x_3, -y_3)$

Step 3: Plot the points A', B', and C'.

Using the transformed coordinates:

1. Plot $A'(x_1, -y_1)$ on the coordinate plane.
2. Plot $B'(x_2, -y_2)$ on the coordinate plane.
3. Plot $C'(x_3, -y_3)$ on the coordinate plane.

Step 4: Connect the points.

Once the points $A'$, $B'$, and $C'$ are plotted, connect them to form triangle $A'B'C'$.

Result:

You now have triangle $A'B'C'$, which is the reflection of triangle $ABC$ across the x-axis.

---

Would you like to provide the original coordinates of the triangle so we can graph it, or do you have any other questions?

Here are five relative questions to deepen your understanding:

1. How does the transformation $(x, y) \rightarrow (x, -y)$ affect the orientation of the triangle?
2. What happens to a point located directly on the x-axis during this transformation?
3. How would the transformation $(x, y) \rightarrow (-x, y)$ affect the triangle?
4. What are the differences between reflecting a triangle over the x-axis and y-axis?
5. Can you think of a situation where both x and y coordinates change sign in a transformation?

Tip: Always remember, reflecting over the x-axis only changes the sign of the y-coordinate, while reflecting over the y-axis only changes the sign of the x-coordinate.