ACT Math : Midpoint Formula
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Example Questions
Example Question #1 : How To Find The Midpoint Of A Line Segment
In the standard x, y coordinate plane what are the coordinates of the midpoint of a line whose endpoints are (–6, 4) and (4, –6)?
1, 1
–1, 1
–1, –1/2
–1, –1
1, –1
–1, –1
To solve this problem we use the midpoint formula. We find the average of the x and y coordinates. (–6 + 4)/2, (4 + –6)/2 = –1, –1
Example Question #4 : How To Find The Midpoint Of A Line Segment
What is the midpoint of a real number line with points at 
Method A:
To find the midpoint, draw the number line that contains points 
Then calculate the distance between the two points. In this case, the distance between 
Method B:
To find the midpoint, use the midpoint formula:
Example Question #1 : How To Find The Midpoint Of A Line Segment
Janice and Mark work in a city with neatly gridded streets. If Janice works at the intersection of 33rd Street and 7th Avenue, and Mark works at 15th Street and 5th Avenue, how many blocks will they each travel to lunch if they meet at the intersection exactly in between both offices?
Translating the intersections into points on a graph, Janice works at (33,7) and Mark works at (15,5). The midpoint of these two points is found by taking the average of the x-coordinates and the average of the y-coordinates, giving ((33+15)/2 , (5+7)/2) or (24, 6). Traveling in one direction at a time, the number of blocks from either office to 24th street is 9, and the number of blocks to 6th is 1, for a total of 10 blocks.
Example Question #1 : How To Find The Midpoint Of A Line Segment
On the real number line, what is the midpoint between 
On the number line,
We find the midpoint of this distance by dividing it by 2.
To find the midpoint, we add this value to the smaller number or subtract it from the larger number.
The midpoint value will be 
Example Question #2 : How To Find The Midpoint Of A Line Segment
What is the midpoint between 
Using the midpoint formula,
We get:
Which becomes: which becomes
Example Question #10 : How To Find The Midpoint Of A Line Segment
What is the midpoint of a line segment with endpoints 
The midpoint of a line can be found using the midpoint formula, given by:
Thus when we plug in our values we get the midpoint is
Example Question #14 : Midpoint Formula
What is the midpoint of the line with endpoints:
To find the midpoint given two points, use the formula:
Example Question #141 : Algebra
A line segment has endpoints at 
What is the midpoint of the line segment?
The midpoint can be found by using equations that calculate the values of its x- and y-coordinates. The x-coordinate can be found using the following equation:
Likewise, we will calculate the y-coordinate using another formula:
These formulas take the average of each coordinate separately in order to calculate the midpoint. In order to solve our question we will substitute in our given values and solve.
Example Question #142 : Algebra
A school superintendent is observing bus routes of students using a town map overlaid with a coordinate plane. Two students, Jon and Steve, live on the same street. Their houses correspond to the coordinates of (-3, 4) and (5,8), respectively, on the map. If there is a bus stop exactly between their two houses, what are the coordinates of the bus stop on the map?
The midpoint formula must be used to find the midpoint of the line segment joining Jon's and Steve's houses. Use the following formula to find the midpoint:
In this formula, 
In this case, the bus stop is at the following coordinate on the town map:
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