Summary
This math recipe will help you find the distance between two points, whose coordinates are known.
Skill Level
Easy
Time
Approx. 2 min
Ingredients
Coordinates of the two points: \(A(x_1, y_1)\) and \(B(x_2, y_2)\)
Method
To find the distance between \(A\) and \(B\), we’ll simply plug their coordinates into the formula below:
\(AB=\sqrt{(x_1-x_2 )^2+(y_1-y_2)^2}\)
This formula is known as the Distance Formula.
Examples
Example 1 Find the distance between \(P(4, 2)\) and \(Q(1,6)\).
Solution The figure shows the points \(P\) and \(Q\) on the plane.
Let’s use the distance formula straight away.
\(PQ=\sqrt{(4-1)^2+(2-6)^2}\)
\(=\sqrt{3^2+(-4)^2}\)
\(=\sqrt{9+16}\)
\(=\sqrt{25}\)
\(= 5\ units\)
Example 2 Find the distance between the points \(A(-1, 5)\) and \(B(4,-7)\).
Solution The figure shows the points \(A\) and \(B\) on the plane.
Again, we’ll use the distance formula directly.
\(AB=\sqrt{(-1-4)^2+(5-(-7))^2}\)
\(=\sqrt{(-5)^2+12^2}\)
\(=\sqrt{25+144}\)
\(=\sqrt{169}\)
\(= 13\ units\)
That’s it for this recipe. Hope you found it helpful.
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