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Mathematics

Finding a Point Given the Midpoint

This lesson explains how to find the coordinates of an unknown endpoint when you know the other endpoint and the midpoint. We build intuition using the concept of symmetry and equal jumps along a line, before applying the formal midpoint formula in reverse.

A (Start) M (Middle) B (End?)
M=Midpoint between A and BM = \text{Midpoint between } A \text{ and } B
Imagine you are standing at point A, and you know the exact middle of your journey is at point M. How do you find out where you'll end up, at point B?
Step-by-step solver
1

Identify knowns

Identify the coordinates of point A and the midpoint M.

A=(xA,yA),  M=(Mx,My)A = (x_A, y_A), \; M = (M_x, M_y)
2

Set up equations

Use the midpoint formula for x and y components.

Mx=xA+xB2,  My=yA+yB2M_x = \frac{x_A + x_B}{2}, \; M_y = \frac{y_A + y_B}{2}
3

Solve for B

Rearrange the equations to solve for the unknown coordinates of B.

xB=2Mx−xA,  yB=2My−yAx_B = 2M_x - x_A, \; y_B = 2M_y - y_A

Original question

find the coordinate B five me some questions

Follow-up chat

Ask me anything about this lesson. I'll answer using what we just covered.