Question

Point A (12, 4) is the image of point A(3, 1) under a dilation with respect to the origin. What is the constant of dilation?​

Answer 1

We conclude that the constant of dilation is: 4

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 point can be determined by multiplying the coordinates of the original point by a certain scale factor.

Given the point A'(12, 4) is the image of A(3, 1).

It is clear that the image point A'(12, 4) is enlarged 4 times of the original point A(3, 1).

It means the image point A'(12, 4) is determined when the original point A(3, 1) is dilated by a scale factor of 4.

i.e.

A(3, 1) → A'(4(3), 4(1)) → A' (12, 4)

Therefore, the rule of dilation by a scale factor 4 is:

P(x, y) → P'(4x, 4y)

Hence, we conclude that the constant of dilation is: 4