Chapter 1, Problem 18CT

To determine

To find: The coordinate of P.

Answer to Problem 18CT

The coordinate of P is -1

Explanation of Solution

Given information:

Point A has coordinate 2 and point B has coordinate 5. If A is the midpoint of PB

Formula used:

  $\text{Midpoint=}\frac{\text{coordinate}\text{of}\left(\text{last}\text{end}\text{+}\text{first}\text{end}\right)}{\text{2}}$

Calculation:

Consider the below figure

  

Segment

A line segment is basically a part of line which connects two points.

It has definite end points.

It can be extended in both directions without end

In above figure on a number line each point is paired with a number and each number is paired with a point

Point A is paired with 2 and it is a coordinate of point A

Point B is paired with 5 and it is a coordinate of point B

Length of line segment PB is the distance between point P and B

To find the coordinate of point P whose value is let x

Use the midpoint formula;

  $\text{Midpoint=}\frac{\text{coordinate}\text{of}\left(\text{last}\text{end}\text{+}\text{first}\text{end}\right)}{\text{2}}$

Here, last end point B coordinate is 5 and first end point P coordinate is x and midpoint A coordinate is 2.

  $\begin{array}{l}\text{Midpoint}\text{=}\frac{\text{coordinate}\text{of}\left(\text{last}\text{end}\text{+}\text{first}\text{end}\right)}{\text{2}}\\ 2=\frac{\left(5+x\right)}{2}\end{array}$

Multiply both sides of find equation $2=\frac{\left(5+x\right)}{2}by2$

  $\begin{array}{l}2\times 2=\frac{\left(5+x\right)}{2}\times 2\\ 4=5+x\end{array}$

Subtract both sides of find equation $4=5+xby5$

  $\begin{array}{l}4-5=5-5+x\\ -1=x\\ x=-1\end{array}$

Therefore, the coordinate of P is -1

Conclusion:

The coordinate of P is -1