# A line segment is bisected by a line with the equation # 4 y - 2 x = 5 #. If one end of the line segment is at #( 7 , 3 )#, where is the other end?

The other end is

Determine the bisector's slope:

The line that is bisected is:

To determine the equation of the bisected line, use the point-slope form of the equation of a line:

Combine equations [2] and [1] as follows:

To determine the corresponding value of x, use equation [2]:

Apply the midpoint calculations:

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 (4y - 2x = 5), given one end at (7, 3), we can use the midpoint formula.

The midpoint formula states that for two endpoints ((x_1, y_1)) and ((x_2, y_2)), the midpoint is given by (\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)).

First, we need to find the coordinates of the midpoint. Then, knowing one end point and the midpoint, we can find the other end point by doubling the coordinates of the midpoint and subtracting the coordinates of the known end point.

Given the line equation (4y - 2x = 5), we need to find the intersection point of this line with the line segment. We already have one point on the segment, (7, 3), so let's find the point of intersection by solving the system of equations formed by the line (4y - 2x = 5) and the line containing the segment:

[ \begin{cases} 4y - 2x = 5 \ y = \frac{1}{2}x - \frac{5}{2} \end{cases} ]

Solve this system to find the coordinates of the intersection point.

Once you have the coordinates of the intersection point, use them and the given point (7, 3) to find the midpoint. Then, double the coordinates of the midpoint and subtract the coordinates of the known point to find the other end of the line segment.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided 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 one-sided 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 one-sided 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.

- What is the perpendicular bisector of a line with points at A #(-33, 7.5)# and B #(4,17)#?
- What is the orthocenter of a triangle with corners at #(4 ,1 )#, #(1 ,3 )#, and (5 ,2 )#?
- What is the centroid of a triangle with corners at #(5, 1)#, #(4, 9)#, and #(7,2)#?
- What is the centroid of a triangle with corners at #(4, 7 )#, #(1,2 )#, and #(8 , 5 )#?
- A triangle has corners A, B, and C located at #(2 ,5 )#, #(7 ,4 )#, and #(3 , 5 )#, 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
- Step-by-step, in-depth guides
- Readily available 24/7