find the coordinate of the image of the point (-3, -1) dilation with center at the origin, scale factor 2.

a. (1.5, .5)
b. (6, 2)
c. (-6, -2)
d. (-1.5, -.5)

(-3,-1) ---- dilation factor of 2 ----> (-6, -2)

show it by plotting the two points
how does the distance to the origin change ?

To find the coordinate of the image of a point after dilation, you need to multiply the coordinates of the original point by the scale factor.

In this case, the original point is (-3, -1), and the scale factor is 2.

To find the x-coordinate of the image, multiply the x-coordinate of the original point by 2: -3 * 2 = -6.
To find the y-coordinate of the image, multiply the y-coordinate of the original point by 2: -1 * 2 = -2.

Therefore, the coordinate of the image of the point (-3, -1) after dilation with a center at the origin and a scale factor of 2 is (-6, -2).

So, the correct answer is c. (-6, -2).

To find the image of the point (-3, -1) under dilation with a center at the origin and a scale factor of 2, we multiply the coordinates of the point by the scale factor.

The coordinates of the image will be:
(x, y) = (scale factor * x-coordinate, scale factor * y-coordinate)

For the point (-3, -1):
x-coordinate = -3
y-coordinate = -1

Using the scale factor of 2:
x-coordinate of the image = 2 * (-3) = -6
y-coordinate of the image = 2 * (-1) = -2

Therefore, the coordinate of the image is (-6, -2).

The correct answer is c. (-6, -2).