About Endpoint Formula
The midpoint formula and the endpoint formula are connected. A midpoint is a point in the middle/centre of a line connecting two points (also known as endpoints). The midpoint formula can be used to compute the other midpoint given one endpoint and a midpoint. Let's look at the endpoint formula in more detail. For more Maths formulas click on the main page.
Endpoint Formula derivations
The endpoint formula can be used to calculate the values of endpoints in a line segment or a ray. Endpoints are the locations on a line segment or a ray where both the line segment and the ray come to a halt. The line does not continue beyond the endpoints. The midpoint formula is required to calculate the endpoints. The midpoint is the point in the middle of any line that connects the two endpoints.
Let M ((x)m, (y)m) be midpoint for line joining 2 endpoints A ((x)1 , (y)1) & B ((x)2 , (y)2). We can solve for either endpoint using the midpoint formula. The formula can be used to find the coordinates of B given the coordinates of M and A:
(From the midpoint formula)
(x)m = x1+x2 / 2,
(y)m = y1+y2 / 2
(x)2 = 2(x)m - (x)1,
(y)2 = 2(y)m - (y)1
Thus, the endpoint formula is,
Endpoint formula
B((x)2, (y)2) = [2(x)m - (x)1 , 2(y)m - (y)1]
Note: It is not suggested that you memorise this formula; instead, use the midpoint formula to obtain B's coordinates.
Endpoint Formula
We get the endpoint formula by solving the midpoint formula for the points x2 and y2.
Endpoint formula B((x)2, (y)2) = (2(x)m - (x)1, 2(y)m - (y)1)
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