Chapter 5.6, Problem 2QR

To determine

To find: the distance between the points A and B.

Answer to Problem 2QR

The distance between the points A and B is $\sqrt{b^2+a^2}$ .

Explanation of Solution

Given information:

Given data:

  $\text{A}\left(0,a\right)$ and $\text{B}\left(b,0\right)$ .

Formula used:

Newton’s method:

  $d=\sqrt{{\left(\Delta x\right)}^2+{\left(\Delta y\right)}^2}$

Calculation :

To calculate the distance between the points A and B,

First we have to find $\Delta x$ and $\Delta y$ .

  $\begin{array}{l}\Delta x=x_2-x_1=b-0\left[x_2=b{y}_2=0\right]\\ \Delta y=y_2-y_1=0-a\left[x_1=0y_1=a\right]\end{array}$

Therefore,

  $\begin{array}{l}d=\sqrt{{\left(\Delta x\right)}^2+{\left(\Delta y\right)}^2}\\ d=\sqrt{{\left(b-0\right)}^2+{\left(0-a\right)}^2}\\ d=\sqrt{{\left(b\right)}^2+{\left(-a\right)}^2}\\ d=\sqrt{b^2+a^2}\end{array}$

Hence, the distance between the points A and B is $\sqrt{b^2+a^2}$ .