Chapter 5.1, Problem 8PSA

To determine

To Find: The slope of $\overleftrightarrow{CD}$ .

Answer to Problem 8PSA

  $\text{Slope of}\overleftrightarrow{CD}=\frac{11}{2}$

Explanation of Solution

Given:

  

With respect to the origin point A is rotated $90°$ clockwise to the point C and point B is rotated $180°$ clockwise to point D.

Concept Used:

During $180°$ rotation point shows reflection symmetry.

  $\text{Slope of joining the points }\left(x_1,y_1\right)\text{and}\left(x_2,y_2\right)=m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Since, with respect to the origin point A is rotated $90°$ clockwise to the point C and point B is rotated $180°$ clockwise to point D. Thus, we have

  

Here, the coordinate of the points C and D are $\text{C}\left(2,0\right)\text{ and D}\left(0,-11\right)$

  $\begin{array}{l}\text{Slope of joining the points C}\left(2,0\right)\text{ and D}\left(0,-11\right)\text{is}=m=\frac{-11-0}{0-2}=\frac{11}{2}\\ \therefore \text{Slope of}\overleftrightarrow{CD}=\frac{11}{2}\end{array}$

Conclusion:

  $\text{Slope of}\overleftrightarrow{CD}=\frac{11}{2}$