How to find the endpoints of a line segment - ACT Math
Card 0 of 6
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?
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?
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).
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).
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The midpoint of a line segment is 
. If one endpoint of the line segment is 
, what is the other endpoint?
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 
.
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
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Suppose the midpoint of a line segment is 
What are the endpoints of the segment?
Suppose the midpoint of a line segment is
The midpoint of a line segment is found using the formula 
.
The midpoint is given as 
Going through the answer choices, only the points 
and 
yield the correct midpoint of 
.
The midpoint of a line segment is found using the formula
The midpoint is given as
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What is the midpoint of the segment of
between 
and 
?
What is the midpoint of the segment of
between
What is the midpoint of the segment of
between 
and 
?
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:
and 
The midpoint of two points is:
Thus, for our data, this is:
or
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
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If 
is the midpoint of 
and another point, what is that other point?
If
If 
is the midpoint of 
and another point, what is that other point?
Recall that the midpoint's 
and 
values are the average of the 
and 
values of the two points in question. Thus, if we call the other point 
, we know that:
and 
Solve each equation accordingly:
For 
, multiply both sides by 
and then subtract 
from both sides:
Thus, 
For 
, multiply both sides by 2 and then subtract 10 from both sides:
Thus, 
Thus, our point is 
If
Recall that the midpoint's
Solve each equation accordingly:
For 
Thus,
For 
Thus,
Thus, our point is
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If 
is the midpoint of 
and another point, what is that other point?
If
Recall that the midpoint's 
and 
values are the average of the 
and 
values of the two points in question. Thus, if we call the other point 
, we know that:
and 
Solve each equation accordingly:
For 
, multiply both sides by 
:
Thus, 
The same goes for the other equation:
, so 
Thus, our point is 
Recall that the midpoint's
Solve each equation accordingly:
For
Thus,
The same goes for the other equation:
Thus, our point is
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