Question

How do you find the midpoint of $(6,7)$ and $(4,3)?$

Answer 1

Hint: Here, we will use the mid-point theorem. Mid-point Theorem states that the coordinates of the midpoint of the line segment are the average of the coordinates of its endpoints. So, here we will find the average of coordinates of the above two points.

Complete step by step answer:
Let the coordinate $(6,7)$ be point A and the coordinate $(4,3)$ be the point B.
Let us assume that C is the midpoint of the two given points A and B.
The coordinates of A are $(6,7)$ so the x-coordinate is $6$, the first number of the pair.
Similarly, the coordinates of B are $(4,3)$, so the x-coordinate is $4$, the first number of the pair.
Similarly, identify the y-coordinates for the points A and B are $7$ and $3$
Now, the average of these x-coordinates is to add them together and divide the result by two and the average of these y-coordinates is to add them together and divide the result by two.
It can be expressed by the equation
C $ = \left( {\dfrac{{6 + 4}}{2},\dfrac{{7 + 3}}{2}} \right)$
Simplify the above expression –
C$ = \left( {\dfrac{{10}}{2},\dfrac{{10}}{2}} \right)$
Find the factors for the term on numerator.
C$ = \left( {\dfrac{{5 \times 2}}{2},\dfrac{{5 \times 2}}{2}} \right)$
Common factors from the numerator and the denominator cancel each other.
C$ = \left( {5,5} \right)$

The midpoint of the given two points is $(5,5)$

Note: Mid-point of a line segment is also known as the Mid-point Theorem. Be good in basic mathematical simplification. Always remember the common factors from the numerator and the denominator cancel each other. Remember the multiples at least twenty, for an accurate and efficient solution.