Chapter MPS, Problem 10.2MPS

(a)

To determine

To Find: The distance between the Stephanie and Heather.

Answer to Problem 10.2MPS

  $2\sqrt{2}units$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Location of Stephanie}:\left(2,3\right)\\ \text{Location of Heather}:\left(4,1\right)\end{array}$

Formula Used:

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

Calculation:

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

Conclusion:

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

(b)

To determine

To Find: The position of Alex who is between Katie and Angela.

Answer to Problem 10.2MPS

  $\left(3,2\right)$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Location of Stephanie}:\left(2,3\right)\\ \text{Location of Heather}:\left(4,1\right)\end{array}$

Alex is between Stephanie and Heather.

Formula Used:

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

Calculation:

  $\begin{array}{l}\text{Mid-Point}=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ \text{⇒}\left(\frac{\left(2\right)+\left(4\right)}{2},\frac{\left(\left(3\right)+\left(1\right)\right)}{2}\right)\\ \text{⇒}\left(\frac{6}{2},\frac{4}{2}\right)\\ \text{⇒}\left(3,2\right)\end{array}$

Conclusion:

Thus, the position of the Alex is $\left(3,2\right)$ .