Q18. - Geometry

Question

Refer to a number line that is not pictured here. Point $A$ has coordinate 2 and point $B$ has coordinate 5.

If $A$ is the midpoint of $\overline{PB}$, what is the coordinate of $P$?

Step-by-Step Solution

Answer

The required coordinate is $-1$.

Step 1. Make the number line.

Make a number line that consists of two points $A$ and $B$ according to the provided information and a number 0 between $A$ and $B$.

Step 2. Definition of line segment.

A path that is making a connection between two points referred as a line segment. The count of points that are representing the end points is definite. There is no end available on right and left side of the line also the line is expanding toward these directions.  

Step 3. Use the formula of midpoint for the calculation of required coordinate.

The gap that is among the points $P$ and $B$ represents the length that is related to the line segment $PB$.

Consider that the coordinate that represents the point $P$ be $x$.

The formula of the midpoint is $\mathrm{Midpoint}=\frac{\mathrm{coordinate} \mathrm{of} \left(\mathrm{last} \mathrm{end} + \mathrm{fist} \mathrm{end}\right)}{2}$ so by taking last end as 5, first end as $x$ and midpoint as 2, determine the value of $x$.

$$\begin{gathered} 2=\frac{\left(5+x\right)}{2} \\ 4=5+x \\ x=4-5 \\ x=-1 \end{gathered}$$