Question

The coordinates of △ABC△ABC are A(12,8), B(10,18), C(4,16)A(12,8), B(10,18), C(4,16). After a dilation, the coordinates are A'(6,4), B'(5,9), C'(2,8)A′(6,4), B′(5,9), C′(2,8). Find the scale factor.

Answer 1

Answer: $\dfrac{1}{2}$

Step-by-step explanation:

The dilation is a transformation which makes similar shapes.

We know that In two similar geometric figures, the ratio of their corresponding corresponding x-coordinate is known as the scale factor.

For the given situation, the x-coordinate of A in pre-image = 12

The x-coordinate of A' in image = 6

Then , the scale factor for the dilation is given by :-

$k=\dfrac{6}{12}=\dfrac{1}{2}$

Hence, the scale factor = $\dfrac{1}{2}$

Answer 2

The scale factor is 1/2 because when you multiply the x and y-coordinates of each point by 1/2, you will get the coordinates of the new dilated points.