Question

A dilation has center (0,0). Find the image of the point LC-5,0) for the scale factor 8.​

Answer 1

The image of the point C(-5,0) for the scale factor 8 is: C'(-40, 0)

Explanation:

Given the coordinates of the point

• C(-5, 0)

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

• If the scale factor > 1, the image is enlarged

• If the scale factor is between 0 and 1, it gets shrunk

• If the scale factor = 1, the object and the image are congruent

Rule to calculate the dilation by a scale factor 8 centered at the origin

P(x, y) → P'(8x, 8y)

Here, P'(8x, 8y) is the image of P(x, y).

It means the coordinates of the image can be determined by multiplying the coordinates of the original point by 8.

Thus,

C(-5, 0) → C'(8(-5), 8(0)) = C'(-40, 0)

Therefore,

The image of the point C(-5,0) for the scale factor 8 is: C'(-40, 0)