Question

A dilation maps ABC onto A’B’C if AC = 24 cm A’C =6 cm and BC =30 cm then B’C’ equals?

Answer 1

The length of B'C' after a dilation with a scale factor of 1/4 is 7.5 cm.

Step-by-step explanation:

If a dilation maps triangle ABC onto triangle A'B'C' and we know that AC = 24 cm and A'C' = 6 cm, then the scale factor of the dilation is 6/24, which simplifies to 1/4. To find B'C', we use the same scale factor, because dilations maintain proportionality. Since BC = 30 cm, then B'C' can be calculated as follows:

B'C' = BC × Scale Factor = 30 cm × (1/4) = 7.5 cm.

Therefore, after the dilation, the length of B'C' is 7.5 cm.

Answer 2

Since A'C' is 1/4 of AC in length, we can see that the dilation has a scale factor of 1/4. This means that all corresponding lengths on the image (A'B'C') will be 1/4 of their lengths on the pre-image (ABC).

So, if BC is 30 cm in ABC, then B'C' will be 1/4 of 30 cm, which is:

B'C' = (1/4) * 30 cm = 7.5 cm

Therefore, B'C' is 7.5 cm.