Question

So for dilation when it says to dilate 1/3 how do I solve that (ex. 18, 9)

Answer 1

The image of A(18, 9) after dilation by a scale factor of 1/3 will be: A'(6, 3).

Explanation:

Let suppose the given point is A(18, 9)

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 1/3 centered at the origin

P(x, y) → P'(1/3x, 1/3y)

Here, P'(1/3, 1/3y) 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 1/3.

Thus,

A(18, 9) → A'(1/3(18), 1/3(9)) = A'(6, 3)

Therefore, the image of A(18, 9) after dilation by a scale factor of 1/3 will be: A'(6, 3).