Question

If point M was located at (4, -2) and was
dilated to M'(6,-3), which dilation rule below
would make the dilation true?
A. (x,y) —> (x + 6, y-3)
B. (X,Y)—>(x,y)
C. (x,y) → (0.6x, 0.6y)
D. (x, y) —>(3/2x3/2y)

Answer 1

Answer:

The rule to calculate the dilation by a scale factor 1/3 centered at the origin

(x, y) → (3/2x, 3/2y)

Hence, option D is correct.

Step-by-step explanation:

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

The coordinates of the image can be determined by multiplying the coordinates of the original point by a given scale factor.

Given that the point M was located at (4, -2) and was dilated to M'(6,-3).

It means if we multiply the coordinates of the original point M(4, -2) by 3/2, we get the image point M'(6, -3).

i.e.

M(4, -2) → M'(3/2(4), 3/2(-2)) → M'(6, -3)

In other words, the image M'(6, -3) is obtained after the dilation by a scale factor 3/2 centered at the origin.

Therefore,

The rule to calculate the dilation by a scale factor 1/3 centered at the origin

(x, y) → (3/2x, 3/2y)

Hence, option D is correct.