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.
