Question

What is the image of point (3, -2) under a dilation of 4 with respect to the origin?

a) (12, -8)
b) (3/4, -1/2)
c) (1.5, -1)
d) (4, -8)

Answer 1

The image of point (3, -2) under a dilation of 4 with respect to the origin is (12, -8). The correct answer is a.

Step-by-step explanation:

The image of point (3, -2) under a dilation of 4 with respect to the origin can be found by multiplying the coordinates of the original point by the scale factor of the dilation.

To calculate the image of the point, we use the formula:

• Image of x-coordinate = scale factor × original x-coordinate
• Image of y-coordinate = scale factor × original y-coordinate

Using the coordinates (3, -2) and the scale factor 4:
Image of x-coordinate = 4 × 3 = 12
Image of y-coordinate = 4 × (-2) = -8

Therefore, the image of point (3, -2) under a dilation of 4 with respect to the origin is (12, -8). Hence the correct option is a.