Subjects

Pre-Calculus

Complex Numbers

Distance and Midpoint of Complex Numbers

Pre-Calculus

Dec 3, 2025

2 pages

Midpoint Formula Explained (Analytic Geometry)

Jezriel Ortiz @jezrielortiz

Finding the midpoint between two points is a key skill in coordinate geometry. It's a straightforward calculation that... Show more

$Midpoint between two points. If points A and B are the two points then $M = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ M B $(x_2,y_2)$ A $(x$

Finding the Midpoint Between Two Points

Ever wondered how to find the exact middle of a line connecting two points? The midpoint formula makes this super easy! When you have two points A(x₁, y₁) and B(x₂, y₂), the midpoint M is calculated using

M = $($x_1+x_2$)/2, ($y_1+y_2$)/2$

This formula simply averages the x-coordinates and y-coordinates of the two points. Let's see it in action to find the midpoint between A(2,3) and B(8,-4), we plug these values into our formula

M = (($2+8$)/2, ($3+(-4)$)/2) = (5, -1/2)

Pro Tip When finding midpoints, always double-check your arithmetic! A common mistake is forgetting the negative sign when adding y-coordinates with different signs.

$Midpoint between two points. If points A and B are the two points then $M = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ M B $(x_2,y_2)$ A $(x$

Working Backward with Midpoints

Sometimes you'll know the midpoint and need to find an unknown endpoint. This requires working the midpoint formula in reverse, which you can totally handle!

For example, if R(3,1) is the midpoint between (-1,4) and (h,k), we set up equations using our formula

3 = $-1+h$ /2 → multiply both sides by 2 → 6 = -1+h → h = 7
1 = $4+k$ /2 → multiply both sides by 2 → 2 = 4+k → k = -2

In geometric problems like rectangles and rhombuses, midpoints help us find missing vertices. For a rhombus QRSP with three known vertices Q(9,6), R(-2,4), and P(4,-4), we can find S(a,b) by recognizing that the diagonals of a rhombus bisect each other.

Remember In any four-sided shape problem, drawing a quick sketch on your coordinate plane can help you visualize the solution before diving into calculations.

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Subjects

Pre-Calculus

Complex Numbers

Distance and Midpoint of Complex Numbers

Pre-Calculus

•

Dec 3, 2025

•

2 pages

Midpoint Formula Explained (Analytic Geometry)

Jezriel Ortiz

@jezrielortiz

Finding the midpoint between two points is a key skill in coordinate geometry. It's a straightforward calculation that helps us locate the exact center of a line segment connecting two points on a coordinate plane.

$Midpoint between two points. If points A and B are the two points then $M = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ M B $(x_2,y_2)$ A $(x$

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Finding the Midpoint Between Two Points

M = $($x_1+x_2$)/2, ($y_1+y_2$)/2$

This formula simply averages the x-coordinates and y-coordinates of the two points. Let's see it in action: to find the midpoint between A(2,3) and B(8,-4), we plug these values into our formula:

M = (($2+8$)/2, ($3+(-4)$)/2) = (5, -1/2)

Pro Tip: When finding midpoints, always double-check your arithmetic! A common mistake is forgetting the negative sign when adding y-coordinates with different signs.

$Midpoint between two points. If points A and B are the two points then $M = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ M B $(x_2,y_2)$ A $(x$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Working Backward with Midpoints

Sometimes you'll know the midpoint and need to find an unknown endpoint. This requires working the midpoint formula in reverse, which you can totally handle!

For example, if R(3,1) is the midpoint between (-1,4) and (h,k), we set up equations using our formula:

3 = $-1+h$ /2 → multiply both sides by 2 → 6 = -1+h → h = 7
1 = $4+k$ /2 → multiply both sides by 2 → 2 = 4+k → k = -2

Remember: In any four-sided shape problem, drawing a quick sketch on your coordinate plane can help you visualize the solution before diving into calculations.