A line segment is bisected by a line with the equation #  4 y + x = 1 #. If one end of the line segment is at #( 7 , 2 )#, where is the other end?
The other end is at
Let's write the given line in the form
The general equation of lines perpendicular to this line is:
To find the value of c, substitute 7 for x and 2 for y:
The equation of the bisected line segment is:
The midpoint is at the intersection of of these two lines:
Multiply equation [1] by 4 and subtract from equation [2]
Let
The y coordinate of the other end of the line,
To find the corresponding x coordinate, substitute
The other end is at
Here is a graph of two lines and two points:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the other end of the line segment bisected by the line with the equation ( 4y + x = 1 ), given that one end is at (7, 2), follow these steps:

Find the midpoint of the line segment using the given point (7, 2) and the equation of the line.

Use the midpoint formula to find the coordinates of the midpoint.

Use the fact that the line bisects the segment to find the other end of the segment.
Here are the detailed steps:

Find the midpoint:
 The midpoint formula for a line segment with endpoints ((x_1, y_1)) and ((x_2, y_2)) is given by: [ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ]
 Given one end of the segment as (7, 2), and since the line bisects the segment, the midpoint lies on the line. Plug in these values into the equation ( 4y + x = 1 ) to find the (x)coordinate of the midpoint.

Once you find the (x)coordinate of the midpoint, substitute it back into the equation of the line to find the corresponding (y)coordinate.

The coordinates of the other end of the line segment are now determined, consisting of the midpoint you found and the given endpoint (7, 2).
Perform these calculations to find the coordinates of the other end of the line segment bisected by the given line.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 A line segment is bisected by a line with the equation # 2 y 4 x = 1 #. If one end of the line segment is at #(3 ,8 )#, where is the other end?
 In the figure below, find #bar(AE)# if #bar(AC)# is a perpendicular bisector of #bar(DE)#?
 In the plane of the triangle #ABC# we have #P# and #Q# such that #vec(PC)=3/2vec(BC)#and #vec(AQ)=1/4vec(AC)#,and #C'#is the middle of #[AB]#.How to demonstrate that #P,Q # and #C'# are collinear points with theorem of Menelaus?
 A line segment is bisected by a line with the equation #  2 y + 3 x = 1 #. If one end of the line segment is at #(6 ,3 )#, where is the other end?
 A triangle has corners A, B, and C located at #(4 ,2 )#, #(2 ,6 )#, and #(8 ,4 )#, respectively. What are the endpoints and length of the altitude going through corner C?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7