Q45. - Algebra 2

Question

For Exercises 45 and 46, use the following information. You can use midpoints and slope to describe some transformations. Suppose point A is the image when point A is reflected over the line with equation $y=x$.

Where is the midpoint of$\overline{AA\text{'}}$?

Step-by-Step Solution

Answer

The midpoint of $\overline{AA\text{'}}$will lie on the line of reflection, that is$y=x$.

Step 1 .Given

Suppose point A’ is the image when point A is reflected over the line with equation $y=x$.

Step 2 .To determine

We have to find the location of the midpoint of$\overline{AA\text{'}}$.

Step 3. Calculation

We know for a reflection every point and its image are equidistance from the line of reflection.

That means the midpoint of $\overline{AA\text{'}}$will lie on the line of reflection, that is$y=x$.