How do you find equations for medians

I will assume you are dealing with a triangle where the coordinates of the vertices are known.

A median is a straight line from a vertex to the midpoint of the opposite side.

So pick a side, find the midpoint of that side.
Now you have a pair of points, the vertex and the opposite midpoint.

Proceed with finding the equation of a straight line if you are given 2 points.

BTW, did you know that you can quickly find the centroid, the intersection of the medians, by (sum of x coordinates/3,sum of y coordinates/3) ?

You could find that point in combination with the 3 vertices to find the 3 medians.

To find the equation for a median in a geometric figure, follow these steps:

1. Identify the geometric figure: Determine the type of figure for which you want to find the equation of the median. For example, if you have a triangle, you'll be finding the equation of a median in a triangle.

2. Find the coordinates of the vertices: Determine the coordinates of the vertices of the geometric figure. In the case of a triangle, you'll need the coordinates of all three vertices.

3. Determine the midpoint of the side: Calculate the midpoint of the side opposite the vertex where you want to find the median. To find the midpoint, average the x-coordinates and the y-coordinates of the two endpoints of that side.

4. Find the equation of the line: Use the slope-intercept form (y = mx + b) to find the equation of the median. The slope (m) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Then, substitute the slope and the coordinates of the midpoint into the equation and solve for b (the y-intercept).

5. Write the equation: Once you have the values of m and b, you can write the equation in slope-intercept form (y = mx + b).

Repeat these steps for each median you want to find. Medians in other geometric figures, such as quadrilaterals or other polygons, will follow similar principles, but the number of vertices and sides may differ.

Remember that the equation of a median represents a line passing through the vertex to the midpoint of the opposite side in a geometric figure.