Question

a triangle is reflected over the y-axis and then translated 3 units up. If the original coordinates of the triangle's vertices are (2,1), (4,3) and (3,5) what are the coordinates of the vertices after the transformation

Answer 1

To find the new coordinates of the triangle's vertices after the described transformations, we will follow these steps:

1. **Reflect the triangle over the y-axis:**
To reflect a point \((x, y)\) over the y-axis, the new coordinates become \((-x, y)\).

Let's apply this reflection to each vertex:
- For the vertex \((2, 1)\):
\((-2, 1)\)
- For the vertex \((4, 3)\):
\((-4, 3)\)
- For the vertex \((3, 5)\):
\((-3, 5)\)

After reflection, the new coordinates of the vertices are:
- \((-2, 1)\)
- \((-4, 3)\)
- \((-3, 5)\)

2. **Translate the triangle 3 units up:**
To translate a point \((x, y)\) 3 units up, we add 3 to the y-coordinate. The new coordinates become \((x, y + 3)\).

Now we apply the translation to the reflected points:
- For \((-2, 1)\):
\((-2, 1 + 3) = (-2, 4)\)
- For \((-4, 3)\):
\((-4, 3 + 3) = (-4, 6)\)
- For \((-3, 5)\):
\((-3, 5 + 3) = (-3, 8)\)

So, the coordinates of the vertices after the transformation are:
- \((-2, 4)\)
- \((-4, 6)\)
- \((-3, 8)\)