Chapter 9, Problem 21CR

a.

To determine

To calculate: Theangle in degrees to be rotated counter clockwise to be at vertex $(0,-4)$ .

Answer to Problem 21CR

The measure of angle in degrees to be rotated counter clockwise to be at vertex $(0,-4)$ is $7^{\circ }$ .

Explanation of Solution

Given information:

  $A=(2\sqrt{3},2)$

Point A is rotated ${127}^{\circ }$ clockwise about the origin to point B .

Formula used:

The angle of each quadrant is ${90}^{\circ }$ .

Calculation:

  

$\Delta AOD$ is triangle with angles ${30}^{\circ },{60}^{\circ }$ and ${90}^{\circ }.$

  $m\angle AOD+m\angle DOC={120}^{\circ }$

Point A is rotated ${127}^{\circ }$ clockwise about the origin to point B .

The measure of angle in degrees to be rotated counter clockwise to be at $(0,-4)$

  $\begin{array}{l}={127}^{\circ }-{120}^{\circ }\\ =7^{\circ }\end{array}$

b.

To determine

To find: The coordinates of the point of reflection.

Answer to Problem 21CR

The coordinates of the point of reflection is $(2\sqrt{3},-4)$ .

Explanation of Solution

Given information:

Point $A=(2\sqrt{3},2)$ is reflected over a line parallel to the x -axis and one unit below the axis.

Calculation:

  

The x coordinate of point A remains same. The reflected line is one unit below x axis.

One unit is 4 and is along negative y axis.

Thus, A $(2\sqrt{3},-4)$