Distance Formula Math Example 3

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Example 3

medium
Show that the triangle with vertices A(0,0)A(0, 0), B(3,4)B(3, 4), and C(6,0)C(6, 0) is isosceles.

Solution

  1. 1
    Find AB=(3−0)2+(4−0)2=9+16=5AB = \sqrt{(3-0)^2 + (4-0)^2} = \sqrt{9 + 16} = 5.
  2. 2
    Find BC=(6−3)2+(0−4)2=9+16=5BC = \sqrt{(6-3)^2 + (0-4)^2} = \sqrt{9 + 16} = 5.
  3. 3
    Find AC=(6−0)2+(0−0)2=6AC = \sqrt{(6-0)^2 + (0-0)^2} = 6.
  4. 4
    Since AB=BC=5AB = BC = 5, the triangle is isosceles.

Answer

AB=BC=5, so the triangle is isosceles.AB = BC = 5 \text{, so the triangle is isosceles.}
The distance formula lets us verify geometric properties algebraically. Two equal sides confirm an isosceles triangle.

About Distance Formula

A formula for finding the distance between two points in the coordinate plane, derived directly from the Pythagorean theorem.

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More Distance Formula Examples

Example 1 easy

Find the distance between the points [formula] and [formula].

Example 2 medium

Find the distance between [formula] and [formula].

Example 4 medium

Find the points on the [formula]-axis that are [formula] units away from the point [formula].

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