Chapter 1.1, Problem 32E

a)

To determine

Tograph : the given points in the coordinate axis.

Explanation of Solution

Given information : we have the given points are $\left(1,12\right)and\left(6,0\right)$

Graph :

The plotting of the points is shown in the graph below

  

Interpretation :

The point $\left(1,12\right)$ is shown by blue dot and point $\left(6,0\right)$ is shown by red dot.

b)

To determine

To find : the distance between two given points.

Answer to Problem 32E

The distance between given points is $13$ units.

Explanation of Solution

Given information : we have the given points are $\left(1,12\right)and\left(6,0\right)$

Let the points be $A\left(1,12\right)andB\left(6,0\right)$

We know that the distance between two points $A\left(x_1,y_1\right)andB\left(x_2,y_2\right)$ is given by

  $AB=\sqrt{{\left(x_1-x_2\right)}^2+{\left(y_1-y_2\right)}^2}$

Now, using the distance formula we get

  $\begin{array}{c}AB=\sqrt{{\left(1-6\right)}^2+{\left(12-0\right)}^2}\\ =\sqrt{{\left(-5\right)}^2+{\left(12\right)}^2}\\ =\sqrt{25+144}\\ =\sqrt{169}\\ =13\end{array}$

Therefore, the distance between given points is $13$ units.

c)

To determine

To find : the midpoint of the line segment joining the points

Answer to Problem 32E

The midpoint between given points is $P\left(x,y\right)=\left(\frac{7}{2},6\right)$

Explanation of Solution

Given information : we have the given points are $\left(1,12\right)and\left(6,0\right)$

Let the points be $A\left(1,12\right)andB\left(6,0\right)$ and $P\left(x,y\right)$ be the midpoint.

We know that the midpoint between two points $A\left(x_1,y_1\right)andB\left(x_2,y_2\right)$ is given by

  $P\left(x,y\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Now, using the distance formula we get

  $\begin{array}{c}P\left(x,y\right)=\left(\frac{1+6}{2},\frac{12+0}{2}\right)\\ =\left(\frac{7}{2},\frac{12}{2}\right)\\ =\left(\frac{7}{2},6\right)\end{array}$

Therefore, the midpoint between given points is $P\left(x,y\right)=\left(\frac{7}{2},6\right)$