Chapter 4, Problem 9RP

a)

To determine

To calculate: Coordinates of M

Answer to Problem 9RP

(9,4)

Explanation of Solution

Given information: Coordinates of A, B, C.

Formula used: Midpoint formulas, distance formula, slope of segment joining two points.

Calculation:

  $\because$ M is midpoint, by midpoint formula.

  $\begin{array}{l}M\left(\frac{3+15}{2},\frac{1+7}{2}\right).\\ \therefore M(9,4)\end{array}$

b)

To determine

To calculate: Slope of BC

Answer to Problem 9RP

  $\frac{1}{2}$

Explanation of Solution

Given information: Coordinates of A, B, C.

Formula used: Midpoint formulas, distance formula, slope of segment joining two points.

Calculation:

Slope of $BC=\frac{7-1}{15-2}=\frac{1}{2}$

c)

To determine

To calculate: To find whether $AR\parallel BC$ or not.

Answer to Problem 9RP

AR is not parallel to BC as their slopes are unequal.

Explanation of Solution

Given information: Coordinates of A, B, C.

Formula used: Midpoint formulas, distance formula, slope of segment joining two points.

Calculation:

Slope of $AR=\frac{8-4}{11-2}=\frac{4}{9}$

d)

To determine

To calculate: Slope of altitude from A to BC.

Answer to Problem 9RP

-2

Explanation of Solution

Given information: Coordinates of A, B, C.

Formula used: Midpoint formulas, distance formula, slope of segment joining two points.

Calculation:

Slope of $BC=\frac{1}{2}$

  $\therefore$ Slope of altitude = -2.

e)

To determine

To calculate: Length of segment AM.

Answer to Problem 9RP

7

Explanation of Solution

Given information: Coordinates of A, B, C.

Formula used: Midpoint formulas, distance formula, slope of segment joining two points.

Calculation:

Slope of $AM=\sqrt{{(4-4)}^2+{(9-2)}^2}=7$