Length of a Line

Finding the Length of a Line segment is useful for finding the distance between 2 separate coordinates/endpoints on a graph. This is very similar to finding the hypoteneuse of a triangle. It can be expressed using the formula:

\(d = \sqrt{(x₂ - x₁)^2 + (y₂ - y₁)^2}\)

  • \(d\) represents the distance
  • \(x₁\) and \(y₁\) represent the first set of coordinates
  • \(x₂\) and \(y₂\) reprsent the second set of coordinates


Calculate the length of a line sgement with endpoints \((4,3)\) and \((2,-2)\).

All we need to do to find the line length is plug the coordinates into the formula:

\(d = \sqrt{(2 - 4)^2 + (-2 - 3)^2}\)
\(d = \sqrt{(-2)^2 + (-5)^2}\)
\(d = \sqrt{4 + 25}\)
\(d = \sqrt{29} ≅ 5.4\)

Therefore, we can determine that the length of the line segment is roughly \(5.4\).

Calculate the length of a line segment with endpoints \((-3/4, -2/5)\) and \((1/4, 3/5)\)

The endpoint of the radius of a circle with centre \(\text{C}(2,3)\) is \(\text{D}(5,5)\).
i. Determine the length of the diameter of the circle.
ii. Determine the coordinates of the endpoint \(\text{E}\) of the diameter \(\text{DE}\) of the circle.

The vertices of △\(\text{XYZ}\) are \(\text{X}(-6, 8)\), \(\text{Y}(-2, -4)\) and \(\text{Z}(4,6)\).
i. Determine the exact length of each side of the triangle.
ii. Classify this triangle.