Examples | Exercises

To find the distance between two points in a coordinate plane, if they lie on the same vertical or horizontal line, is determined by their coordinates.

A = (x₁, y₁) and B = (x₂, y₂) are two points on the plane, then let C = (x₂, y₁) as in the figure above. The points A, B, C then form a triangle with a right angle at C. The Pythagorean theorem tells us that

From whence, we obtain the distance formula.

EXAMPLE I

Find the distance between these two points: (2, -3) and (2, 4).

SOLUTION

Use the distance formula and plug in the numbers to where they go. Since x₁ = 2, y₁ = -3, x₂ = 2, and y₂ = 4:
d = SQRT(2 - 2)² + (4 + 3)²
The distance is = 7

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