A. triangle ABC is reflected over the y- axis. What are the coordinates of the reflected triangle?
B. Describe in words what happens to the x- coordinates and y- coordinates of the original triangle's vertices as a result of this reflection.
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A. To find the coordinates of the reflected triangle, we need to flip the sign of the x-coordinate for each vertex. If the original triangle ABC has coordinates (x1, y1), (x2, y2), and (x3, y3), then the reflected triangle A'B'C' will have coordinates (-x1, y1), (-x2, y2), and (-x3, y3).
B. As a result of the reflection over the y-axis, the x-coordinates of the original triangle's vertices will change sign, while the y-coordinates will remain the same. This means that the x-coordinates will be negated, but the y-coordinates will stay as they are.
To find the coordinates of the reflected triangle when triangle ABC is reflected over the y-axis, you need to reverse the sign of the x-coordinates while keeping the y-coordinates unchanged.
Let's assume the original triangle ABC has the following coordinates:
Point A: (x₁, y₁)
Point B: (x₂, y₂)
Point C: (x₃, y₃)
When triangle ABC is reflected over the y-axis, the resulting triangle, let's call it A'B'C', will have the following coordinates:
Point A': (-x₁, y₁)
Point B': (-x₂, y₂)
Point C': (-x₃, y₃)
In summary, for a reflection over the y-axis, the x-coordinates of the original triangle's vertices are negated, while the y-coordinates remain the same.
Therefore, for part B of the question:
- The x-coordinates of the original triangle's vertices change their signs.
- The y-coordinates of the original triangle's vertices remain the same.