Question

Triangle QRS is dilated by a scale factor of 6 to form triangle Q'R'S'. Side R'S' R'S' measures 18. What is the measure of side RS?

Answer 1

The measure of side RS in triangle QRS before the dilation is 3 units. This is calculated by dividing the length of side R'S' after the dilation, which is 18 units, by the scale factor of 6.

Step-by-step explanation:

If triangle QRS is dilated by a scale factor of 6 to form triangle Q'R'S' and side R'S' measures 18 units, we can determine the measure of side RS by using the properties of a dilation in geometry. Dilation is a transformation that produces an image that is the same shape as the original, but a different size. The scale factor tells us how much larger or smaller the image is compared to the original.

To find the length of side RS, we need to divide the length of the dilated side R'S' by the scale factor. Here is the step-by-step explanation:

1. Determine the scale factor between triangle QRS and triangle Q'R'S', which is given as 6.
2. Know the measure of side R'S', which is 18 units.
3. Divide the measure of side R'S' by the scale factor to find the original length of side RS: RS = R'S' ÷ scale factor = 18 units ÷ 6 = 3 units.

Thus, the measure of side RS is 3 units.