Chapter SH, Problem 10.5.1EP

To determine

The distance between each pair of points and round to the nearest tenth if necessary.

Answer to Problem 10.5.1EP

The distance between each pair of point is $7.3$ round to the nearest tenth.

Explanation of Solution

Given:

Two Points $A\left(2,6\right),B\left(-4,2\right)$

Concept Used:

The distance formula is used to calculate the distance between two points which is given by

  $d=$ (x1−x2)2+(y1−y2)2

Calculation:

As the given two pints are $A\left(2,6\right),B\left(-4,2\right)$

Now Consider,

  $\begin{array}{l}A(2,6)=\left(x1,y1\right)\\ B(-4,2)=(x2,y2)\end{array}$

Substitute all the given values from the above distance formula given,

  $d(A,B)=\sqrt{{\left(x1-x2\right)}^2+{\left(y1-y2\right)}^2}$

  $=\sqrt{{\left(2-\left(-4\right)\right)}^2+{\left(6-2\right)}^2}$

  $=\sqrt{{\left(6\right)}^2+{\left(4\right)}^2}$

  $=\sqrt{36+16}$ $=\sqrt{52}$

  $d(A,B)=7.21$ $\approx 7.3$

  $d(A,B)=7.3$

Conclusion:

Hence, the distance between each pair of point is. $7.3$ round to the nearest tenth.