Question

If the pre image coordinate is G (-8, -2) what is the image coordinate with a dilation of k=LaTeX: \frac{1}{2}1 2?

A. G' (-16, -4)

B. G' (-6, 0)

C. G' (-4, -1)

D. None of the Above

Answer 1

Option G'(-4, -1) is correct.

Explanation:

Given the coordinates of the point

• G (-8, -2)

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 1/2 centered at the origin

P(x, y) → P'(1/2x, 1/2y)

Here, P'(1/2, 1/2y) 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 1/2.

Thus,

G (-8, -2) → A'(1/2(-8), 1/2(-2)) = G'(-4, -1)

Therefore, the image coordinates of G (-8, -2) after dilation by a scale factor of 1/2 will be: G'(-4, -1)

Thus, option G'(-4, -1) is correct.