Some coordinate geometry questions may require you to find the midpoint of line segments in the coordinate plane. To find a point that is halfway between two given points, get the average of the x-values and the average of the y-values.
The midpoint between the two points (x1,y1) and (x2,y2) is given by the formula
The midpoint of the points A(1,4) and B(5,6) is
We can use the midpoint formula to find the midpoint when given two endpoints.
Find the midpoint of the two points A(1, -3) and B(4, 5).
Midpoint = = (2.5, 1)
We can use the midpoint formula to find an endpoint when given a midpoint and another endpoint.
M(3, 8) is the midpoint of the line AB. A has the coordinates (-2, 3), Find the coordinates of B.
Let the coordinates of B be (x, y)
Coordinates of B = (8, 13)
The following video gives an example of finding a missing endpoint if given the midpoint and another endpoint.
We can use the Pythagorean theorem to prove the midpoint formula.
The following video gives a proof of the midpoint formula using the Pythagorean Theorem.
In the following video we prove the Midpoint Formula by using the distance formula to show the midpoint creates two congruent segments & the slope formula to show that the coodinate of the midpoint is located on the line segment.
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