Chapter B, Problem 1E

To determine

To find: The distance between the given points.

Answer to Problem 1E

The distance between the points is 5.

Explanation of Solution

Given:

The points are $\left(1,1\right),\left(4,5\right)$.

Formula used:

$\begin{array}{l}{\text{The distance between the points P}}_1\left(x_1,y_1\right){\text{ and P}}_2\left(x_2,y_2\right)\text{is}\\ \left|P_1{P}_2\right|=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\end{array}$

Calculation:

Let the given points be,

$\left(x_1,y_1\right)=\left(1,1\right)\text{ and }\left(x_2,y_3\right)=\left(4,5\right)$.

Use the above mentioned formula to find the distance between the points

$\begin{array}{c}\left|P_1{P}_2\right|=\sqrt{{\left(4-1\right)}^2+{\left(5-1\right)}^2}\\ =\sqrt{{\left(3\right)}^2+{\left(4\right)}^2}\\ =\sqrt{9+16}\\ =\sqrt{25}\end{array}$

So, the distance becomes,

$\sqrt{25}=5$

Thus, the equation for x for the given modulus function is 5.