Question

A triangle has vertices `\left(-3,\ -2\right),\ \left(0,\ 5\right)`and `\left(4,\ 2\right)`.What are the vertices after translating the triangle 3 units up?

Answer 1

To translate a triangle vertically upwards, we need to add the same value to the y-coordinates of each vertex. In this case, we will add 3 units to each y-coordinate of the triangle's vertices.

The original vertices of the triangle are:
1. \((-3, -2)\)
2. \((0, 5)\)
3. \((4, 2)\)

Now let's translate each vertex:

1. For the vertex \((-3, -2)\):
\[
\text{New vertex} = (-3, -2 + 3) = (-3, 1)
\]

2. For the vertex \((0, 5)\):
\[
\text{New vertex} = (0, 5 + 3) = (0, 8)
\]

3. For the vertex \((4, 2)\):
\[
\text{New vertex} = (4, 2 + 3) = (4, 5)
\]

So, the new vertices of the triangle after translating it 3 units up are:

- \((-3, 1)\)
- \((0, 8)\)
- \((4, 5)\)