Chapter 9.2, Problem 4PSA

a

To determine

To find:The coordinates of point D

Answer to Problem 4PSA

The coordinates of point D are $D=(0,4)$

Explanation of Solution

Given information:The following information has been given

Origin is the center of the circle

Radius is four units

Point G and D lie on X and Y axes respectively

Calculation:We know that the radius is four units. Also, we know that the point D lies on the Y axis.

Now, as the radius is four units, point D will also be the same distance away from the origin. Hence, the coordinates of point D can be given by

  $D=(0,4)$

b

To determine

To find:The area of sector DOG

Answer to Problem 4PSA

The area of sector DOG is $12.566{\text{ units}}^2$

Explanation of Solution

Given information:The following information has been given

Origin is the center of the circle

Radius is four units

Point G and D lie on X and Y axes respectively

Calculation:We know that the measure of an arc is the degree measure subtended by the arc to the center of the circle. Hence, the angle subtended by the arc is same as the angle between the X and Y axes. Hence, we can say that

  $m\stackrel{⌢}{DG}={90}^0$

We know that the area of the sector can be found by

  $\stackrel{⌢}{DOG}=\pi r^2\frac{{90}^0}{{360}^0}$

Hence, we substitute the value of radius as four units, and we get

  $\stackrel{⌢}{DOG}=\frac{16\pi }{4}=12.566$