Chapter 3.8, Problem 15PSB

a

To determine

To find : The coordinates of point S.

Answer to Problem 15PSB

The coordinates are $S=(4,0)$

Explanation of Solution

Given information : QS is the altitude of PR

Formula used : Altitude is perpendicular to the base side

Calculation : We know that QS is the altitude of PR. Thus, we can say that

  $Q(x,y)=S(x,0)$

Thus, we know that $Q(x,y)=(4,9)$ . Hence, we can say that

  $S=(4,0)$

b

To determine

To explain : The reason for $PS=SR$ is to be explained

Answer to Problem 15PSB

The altitude of isosceles triangle is a median as well

Explanation of Solution

Given information : The following information has been given

  $PQ=QR$

From $PQ=QR$ , we can say that triangle PQR is an isosceles triangle

Thus, we know that altitude of isosceles triangle is a median as well. Hence, we can say that

  $PS=SR$

c

To determine

To calculate : The coordinates of point R.

Answer to Problem 15PSB

The coordinates are $R=(10,0)$

Explanation of Solution

Given information : The following information has been given

  $PS=SR$

Formula used : Linear addition of coordinates is used

Calculation : We know that $PS=SR$ . Thus, we can say that

  $PS=SR=6$

Thus, we know that $P(x,y)=(-2,0)$ . Hence, we can say that

  $R=(10,0)$

d

To determine

To calculate : The area of triangle PQR.

Answer to Problem 15PSB

The area is $A=54$

Explanation of Solution

Given information : The following information has been given

QS is the altitude of PR

  $QS=9$

  $PR=12$

Formula used : The area of a triangle is

  $A=\frac{1}{2}(base)(height)$

Calculation : We know that QS is the height and PR is the base of the triangle. Thus, we can say that

  $A=\frac{1}{2}(12)(9)=54$

The area is $A=54$