Dilate triangle ABC with vertices A(-6,6), B(4,8), C(2,10) by a scale factor of 1/2 using a center of dilation of (0,0). Name and label the image points.

To dilate a triangle ABC with a scale factor of 1/2 using a center of dilation at (0,0), follow these steps:

1. Calculate the coordinates of the image points:
- Point A: The image of A is located at (-6 * 1/2, 6 * 1/2) = (-3, 3).
- Point B: The image of B is located at (4 * 1/2, 8 * 1/2) = (2, 4).
- Point C: The image of C is located at (2 * 1/2, 10 * 1/2) = (1, 5).

2. Plot the original and image points on a coordinate plane.
- Point A (-6,6), B(4,8), and C(2,10)
- Image of A (-3,3), B(2,4), and C(1,5)

3. Label the image points as A', B', and C', respectively.

Therefore, the image triangle after dilation with a scale factor of 1/2 and a center of dilation at (0,0) is triangle A'B'C' with vertices A'(-3,3), B'(2,4), and C'(1,5).

To dilate a triangle, we need to multiply the coordinates of each vertex of the original triangle by the scale factor. In this case, the scale factor is 1/2.

Let's start by calculating the new coordinates for each vertex of triangle ABC.

For vertex A(-6, 6):
New x-coordinate = (-6) * (1/2) = -3
New y-coordinate = 6 * (1/2) = 3
So the new coordinate for A is (-3, 3).

For vertex B(4, 8):
New x-coordinate = 4 * (1/2) = 2
New y-coordinate = 8 * (1/2) = 4
So the new coordinate for B is (2, 4).

For vertex C(2, 10):
New x-coordinate = 2 * (1/2) = 1
New y-coordinate = 10 * (1/2) = 5
So the new coordinate for C is (1, 5).

Now let's label the image points of the dilated triangle:

The image point of A is A'(-3, 3).
The image point of B is B'(2, 4).
The image point of C is C'(1, 5).

So, the image points of the dilated triangle ABC with a scale factor of 1/2 and a center of dilation at (0, 0) are A'(-3, 3), B'(2, 4), and C'(1, 5).

just multiply all the coordinates by 1/2