# Midpoint

The midpoint is the halfway point between 2 endpoints of a line segment. Certain line segments, such as medians and right bisectors are found using the midpoint. It can be found using the following formula:

$$\text{midpoint} = (\cfrac{x₁ + x₂}{2}, \cfrac{y₁ + y₂}{2})$$

• $$x₁$$ represents the x-coordinate of the first point
• $$x₂$$ represents the x-coordinate of the second point
• $$y₁$$ represents the y-coordinate of the first point
• y₂ represents the y-coordinate of the second point

Example

Find the midpoint of a line segment with endpoints $$\text{C}(-4, 3)$$ and $$\text{D}(2, -5)$$.

We can plug the coordinates into the formula to determine the midpoint. In this instance, $$\text{C}$$ will represent the first coordinate and $$\text{D}$$ will represent the second coordinate:

midpointCD $$= (\cfrac{-4 + 2}{2}, \cfrac{3 + (-5)}{2})$$

midpointCD $$= (\cfrac{-2}{2}, \cfrac{-2}{2})$$

midpointCD $$= (-1, -1)$$

Therefore, we can determine that the midpoint between points $$\text{C}$$ and $$\text{D}$$ is $$(-1, -1)$$.

Find the midpoint of a line segment with endpoints $$\text{A}(-2/5, -3/4)$$ and $$\text{B}(4/5, 3/4)$$.

The endpoints of the diameter of a circle are $$\text{A}(-5, -3)$$ and $$\text{B}(3, 7)$$. Find the coordinates of the circle's origin.

1.Draw △ABC with vertices $$\text{A}(-8, 0)$$, $$\text{B}(0, 0)$$ and $$\text{C}(0, -8)$$.
2. Construct the midpoints $$\text{AB}$$, $$\text{BC}$$, and $$\text{AC}$$ and label them $$\text{D}$$, $$\text{E}$$, and $$\text{F}$$ respectively. Join the midpoints to form △$$\text{DEF}$$.
3. Show that line segment $$\text{DE}$$ is parallel to the line segment $$\text{AC}$$.