Chapter 1, Problem 22SGR

a.

To determine

To find the distance between C and M

Answer to Problem 22SGR

9

Explanation of Solution

Given information:

C’s location (7,13)

M’s location (3,5)

Formula used:

Distance = $\sqrt{{(x_2^{}-x_1^{})}^2+{(y_2^{}-y_1^{})}^2}$

Calculation: substituting values in the formula

Distance = $\sqrt{{\left(3-7\right)}^2+{\left(5-13\right)}^2}$

Solving further

Distance = $\sqrt{{\left(-4\right)}^2+{\left(-8\right)}^2}$

Solving further

Distance = $\sqrt{16+64}=\sqrt{80}$

Value of the root is

8.9 Or 9

b.

To determine

To find midway between their location

Answer to Problem 22SGR

(5,9)

Explanation of Solution

Given information:

C’s location (7,13)

M’s location (3,5)

Formula used:

Mid-point $M(X,Y)$

For $X=\frac{x_1^{}+x_2^{}}{2}$ , For $Y=\frac{y_1^{}+y_2^{}}{2}$

Calculation: let C(7,13) be $x_{1,}^{}{y}_1^{}$ and M(3,5) be $x_{2,}^{}{y}_2^{}$

Substituting values in the formula\

  $X=\frac{7+3}{2},Y=\frac{13+5}{2}$

Solving further

  $X=\frac{10}{2},Y=\frac{18}{2}$

Solving for the midpoints

  $X=5,Y=9$

Therefore the midpoints are.........(5,9)