Chapter MPS, Problem 10.1MPS

(a)

To determine

To Find: The distance between the Katie and Angela.

Answer to Problem 10.1MPS

  $2\sqrt{13}units$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Location of Katie}:\left(1,-7\right)\\ \text{Location of ANgela}:\left(-5,-3\right)\end{array}$

Formula Used:

  $\text{Distance between two points}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Calculation:

  $\begin{array}{l}\text{Distance between two points}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ \text{⇒}\sqrt{{\left(-5-1\right)}^2+{\left(-3-\left(-7\right)\right)}^2}\\ \text{⇒}\sqrt{{\left(6\right)}^2+{\left(4\right)}^2}.\\ \text{⇒}\sqrt{36+16}\\ \text{⇒}2\sqrt{13}units\end{array}$

Conclusion:

Thus, the distance between them is $2\sqrt{13}units$ .

(b)

To determine

To Find: The mid-point between Katie and Angela

Answer to Problem 10.1MPS

  $\left(-2,-5\right)$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Location of Katie}:\left(1,-7\right)\\ \text{Location of ANgela}:\left(-5,-3\right)\end{array}$

Formula Used:

  $\text{Mid-Point}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Calculation:

  $\begin{array}{l}\text{Mid-Point}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ \text{⇒}\left(\frac{\left(-5\right)+\left(1\right)}{2},\frac{\left(\left(-7\right)+\left(-3\right)\right)}{2}\right)\\ \text{⇒}\left(-2,-5\right)\end{array}$

Conclusion:

Thus, the mid-point is $\left(-2,-5\right)$ .