Question

What are the coordinates of A after a dilation of 2/3 centered at the origin? Question 11 options:

A' =(−3/4, −3/2)

A' = (4/3, 2/3)

A' = (2, 1)

A' =(2/3, 2/3)

Answer 1

The image of A(2, 1) after dilation by a scale factor of 2/3 will be: A'(4/3, 2/3) .

Explanation:

Given

• Point A (2, 1)

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 2/3 centered at the origin

P(x, y) → P'(2/3x, 2/3y)

Here, P'(2/3, 2/3y) 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 2/3.

Thus,

A(2, 1) → A'(2/3(2), 2/3(1)) = A'(4/3, 2/3)

Therefore, the image of A(2, 1) after dilation by a scale factor of 2/3 will be: A'(4/3, 2/3) .