Chapter 11, Problem 12STP

To determine

To find the distance between two points.

Answer to Problem 12STP

  $9.9$ units

Explanation of Solution

Given information:

The two points are $M\left(2,4\right)$ and $N\left(-5,-3\right)$ .

Formula used:

Distance between the two points on a 2-D plane can be calculates using the formula $s=\sqrt{{\left(a_1-b_1\right)}^2+{\left(a_2-b_2\right)}^2}$ where $(a_1,a_2)$ and $(b_1,b_2)$ are the coordinates of the two given points.

Calculation:

Assume $(a_1,a_2)\equiv M\left(2,4\right)$ and $(b_1,b_2)\equiv N\left(-5,-3\right)$

  $s=\sqrt{{\left(a_1-b_1\right)}^2+{\left(a_2-b_2\right)}^2}$

Formula to calculate the distance.

  $=\sqrt{{\left(2-\left(-5\right)\right)}^2+{\left(4-\left(-3\right)\right)}^2}$

Putting the values in the formula.

  $=\sqrt{{\left(2+5\right)}^2+{\left(4+3\right)}^2}$

Removing the inner brackets.

  $=\sqrt{{\left(2+5\right)}^2+{\left(4+3\right)}^2}$

On simplifying the expression.

  $=\sqrt{7^2+7^2}$

Squaring the components inside the square root.

  $=\sqrt{198}$

Simplifying the square.

  $=7\times \sqrt{2}$

Taking $\sqrt{2}=1.41$ for calculation purpose.

  $=7\times 1.41$

Multiplying this, to get the final value.

  $=9.87$

This can be rounded of to the nearest tenth.

  $=9.9$ units.