All GMAT Math Resources
Example Questions
Example Question #1 : Coordinate Geometry
The midpoint of a line segment with endpoints and is . Sove for .
It cannot be determined from the information given.
It cannot be determined from the information given.
The midpoint of a line segment with endpoints is
.
Substitute the coordinates of the endpoints, then set each equation to the appropriate midpoint coordinate.
-coordinate:
-coordinate:
Simplify each, then solve the system of linear equations in two variables:
The two linear equations turn out to be equivalent, meaning that there are infinitely many solutions to the system. Therefore, insufficient information is given to answer the question.
Example Question #841 : Gmat Quantitative Reasoning
Find the midpoint of the points and .
Add the corresponding points together and divide both values by 2:
Example Question #842 : Gmat Quantitative Reasoning
What is the midpoint of and ?
Add the x-values and divide by 2, and then add the y-values and divide by 2. Be careful of the negatives!
Example Question #4 : Coordinate Geometry
Consider segment which passes through the points and .
What are the correct coordinates for the midpoint of ?
Midpoint formula is as follows:
Plug in and calculate:
Example Question #4 : Coordinate Geometry
Segment has endpoints of and . If the midpoint of is given by point , what are the coordinates of point ?
Midpoints can be found using the following:
Plug in our points (-6,8) and (4,26) to find the midpoint.
Example Question #5 : Calculating The Midpoint Of A Line Segment
What are the coordinates of the mipdpoint of the line segment if and
The midpoint formula is
Example Question #3 : Midpoint Formula
The quadrilateral with vertices is a trapezoid. What are the endpoints of its midsegment?
The midsegment of a trapezoid is the segment whose endpoints are the midpoints of its legs - its nonparallel opposite sides. These two sides are the ones with endpoints and . The midpoint of each can be found by taking the means of the - and -coordinates:
The midsegment is the segment that has endpoints (2,2) and (19,2)
Example Question #843 : Gmat Quantitative Reasoning
The midpoint of a line segment with endpoints and is . What is ?
It cannot be determined from the information given.
If the midpoint of a line segment with endpoints and is , then by the midpoint formula,
and
.
The first equation can be simplified as follows:
or
The second can be simplified as follows:
or
This is a system of linear equations. can be calculated by subtracting:
Example Question #5 : Midpoint Formula
If the midpoint of is and is at , what are the coordinates of ?
Midpoint formula is as follows:
In this case, we have x,y and the value of the midpoint. We need to findx' and y'
V is at (2,9) and the midpoint is at (6,7)
and
So we have (10,5) as point U
Example Question #11 : Coordinate Geometry
A line segment has its midpoint at and an endpoint at . What are the coordinates of the other endpoint?
Because we are given the midpoint and one of the endpoints, we know the x coordinate of the other endpoint will be the same distance away from the midpoint in the x direction, and the y coordinate of the other endpoint will be the same distance away from the midpoint in the y direction. Given two endpoints of the form:
The midpoint of these two endpoints has the coordinates:
Plugging in values for the given midpoint and one of the endpoints, which we can see is because it lies to the right of the midpoint, we can solve for the other endpoint as follows:
So the other endpoint has the coordinates