Summary
This math recipe will help you find the mid-point of two points, whose coordinates are known.
Skill Level
Easy
Time
Approx. 1 min
Ingredients
Coordinates of the two points: \(A(x_1, y_1)\) and \(B(x_2, y_2)\)
Method
To find the mid-point \(C\) of \(A\) and \(B\), we’ll simply plug their coordinates into the formula below:
\(C \equiv \left ( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \right ) \)
This formula is sometimes called the Mid-Point Formula.
Examples
Example 1 Find the mid-point of \(P(4, 6)\) and \(Q(-2, 2)\).
Solution The figure shows the points and on the plane.
To find the mid-point \(R\), we’ll use the mid-point formula directly.
\(R \equiv \left ( \frac{4+(-2)}{2},\frac{6+2}{2} \right ) \)
\( \equiv \left ( \frac{2}{2},\frac{8}{2} \right ) \)
\( \equiv (2,4) \)
Example 2 Find the mid-point of \(A(-1, 5)\) and \(B(7, -3)\).
Solution The figure shows the points and on the plane.
To find the mid-point \(C\), we’ll again use the mid-point formula straight away.
\(C \equiv \left ( \frac{-1+7}{2},\frac{5+(-3)}{2} \right ) \)
\( \equiv \left ( \frac{6}{2},\frac{2}{2} \right ) \)
\( \equiv (3,1) \)
That’s it for this recipe. Hope you found it helpful.
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