ACT Math : How to find the endpoints of a line segment
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Example Question #1 : Midpoint Formula
In the standard (x,y) coordinate plane, the midpoint of line XY is (12, –3) and point X is located at (3, 4). What are the coordinates of point Y?
(9, 7)
(21, –10)
(9, –7)
(–4, 11)
(7.5, 0.5)
(21, –10)
To get from the midpoint of (12, –3) to point (3,4), we travel –9 units in the x-direction and 7 units in the y-direction. To find the other point, we travel the same magnitude in the opposite direction from the midpoint, 9 units in the x-direction and –7 units in the y-direction to point (21, –10).
Example Question #1 : Midpoint Formula
The midpoint of a line segment is 
The midpoint formula can be used to solve this problem, where the midpoint is the average of the two coordinates.
We are given the midpoint and one endpoint. Plug these values into the formula.
Solve for the variables to find the coordinates of the second endpoint.
The final coordinates of the other endpoint are 
Example Question #3 : Midpoint Formula
Suppose the midpoint of a line segment is 
The midpoint of a line segment is found using the formula 
The midpoint is given as 
Example Question #4 : Midpoint Formula
What is the midpoint of the segment of
between 
What is the midpoint of the segment of
between 
To find this midpoint, you must first calculate the two end points. Thus, substitute in for 
Then, for 
Thus, the two points in question are:
The midpoint of two points is:
Thus, for our data, this is:
or
Example Question #5 : Midpoint Formula
If 
Recall that the midpoint's 
Solve each equation accordingly:
For 
Thus,
The same goes for the other equation:
Thus, our point is 
Example Question #6 : Midpoint Formula
If 
If 
Recall that the midpoint's 
Solve each equation accordingly:
For 
Thus,
For 
Thus,
Thus, our point is
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