A triangle has vertices with coordinates (2, 0), (3, -1), and (-2, -5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image.

If the scale factor is 3, then

A(2,0) ----> A' (6,0)
B(3,-1) ---> B' (9,-3)
C(-2,-5) --> C' (-6,-15)

Can't get any simpler than that.

Might be a good idea to graph the original triangle and the new triangle.
What do you notice ?

The vertices of triangle ABC are A(3, -6), B(6,3), C(9,-3). Find the image matrix that represents the dilation of triangle ABC centered at the origin with a scale factor of 2/3. Then graph the triangle and its image

To dilate a triangle with a scale factor of 3 with the origin as the center of dilation, we need to multiply the coordinates of each vertex by 3.

Let's calculate the new coordinates, one vertex at a time:

1. First vertex: (2, 0)
Multiply the x-coordinate and the y-coordinate by 3:
New x-coordinate = 2 * 3 = 6
New y-coordinate = 0 * 3 = 0
So, the new coordinates of the first vertex are (6, 0).

2. Second vertex: (3, -1)
Multiply the x-coordinate and the y-coordinate by 3:
New x-coordinate = 3 * 3 = 9
New y-coordinate = -1 * 3 = -3
So, the new coordinates of the second vertex are (9, -3).

3. Third vertex: (-2, -5)
Multiply the x-coordinate and the y-coordinate by 3:
New x-coordinate = -2 * 3 = -6
New y-coordinate = -5 * 3 = -15
So, the new coordinates of the third vertex are (-6, -15).

Therefore, the coordinates of the vertices of the dilated triangle are (6, 0), (9, -3), and (-6, -15).

To find the coordinates of the dilated triangle, we first need to determine the coordinates of each vertex after dilation.

The formula for dilation with respect to the origin is:

(x', y') = (k * x, k * y)

where (x, y) are the original coordinates, (x', y') are the new coordinates after dilation, and k is the scale factor.

Given that the scale factor is 3, we can apply the formula to each vertex to find the new coordinates.

Let's calculate the new coordinates using the given vertices:

For the first vertex (2, 0):

x' = 3 * 2 = 6
y' = 3 * 0 = 0

So, the new coordinates for the first vertex are (6, 0).

For the second vertex (3, -1):

x' = 3 * 3 = 9
y' = 3 * -1 = -3

So, the new coordinates for the second vertex are (9, -3).

For the third vertex (-2, -5):

x' = 3 * -2 = -6
y' = 3 * -5 = -15

So, the new coordinates for the third vertex are (-6, -15).

Therefore, the coordinates of the vertices of the dilated triangle with a scale factor of 3 and the origin as the center of dilation are (6, 0), (9, -3), and (-6, -15).