Q46. - 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$y=x$.

What is the slope of $\overline{AA\text{'}}$? Explain.

Step-by-Step Solution

Answer

The slope of $\overline{AA\text{'}}$is –1.

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 slope of $\overline{AA\text{'}}$.

Step 3. Calculation

Compare $y=x$ with $y=mx+b$.

So, the slope of $y=x$ is 1.

We know that the line joining a point and its image is perpendicular to the line of reflection.

The slope of a perpendicular line is negative reciprocal. So, the slope of $\overline{AA\text{'}}$is $-\frac{1}{1}=-1$.