# 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

Example

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.