Distance Math Example 1

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Example 1

easy
Find the distance between points A(1,2)A(1, 2) and B(4,6)B(4, 6).

Solution

  1. 1
    Step 1: Use the distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}.
  2. 2
    Step 2: Substitute: d=(4−1)2+(6−2)2=32+42d = \sqrt{(4-1)^2 + (6-2)^2} = \sqrt{3^2 + 4^2}.
  3. 3
    Step 3: Calculate: d=9+16=25=5d = \sqrt{9 + 16} = \sqrt{25} = 5.

Answer

d=5d = 5 units
The distance formula is derived from the Pythagorean theorem. The horizontal and vertical separations form the legs of a right triangle, and the distance is the hypotenuse. Here the 3-4-5 right triangle makes the answer a whole number.

About Distance

The length of the shortest path between two points, always a non-negative real number.

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More Distance Examples

Example 2 medium

Find the distance between [formula] and [formula]. Leave your answer in simplest radical form.

Example 3 easy

What is the distance from the origin [formula] to the point [formula]?

Example 4 hard

Find the distance between points [formula] and [formula] in 3D space.

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