# A line segment is bisected by a line with the equation # 2 y + 9 x = 3 #. If one end of the line segment is at #(3 ,2 )#, where is the other end?

The point

Regarding a line whose slope is perpendicular to the specified line

Exchange the x and y coefficients, alter one of the coefficients' signs, and set it equal to any random constant:

The bisected line's equation is as follows:

Equation [1] should be multiplied by 9 and equation [2] by 2:

Combine equations [3] and [4] as follows:

This is the intersection's x coordinate.

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 (2y + 9x = 3), given that one end is at (3, 2), we can use the midpoint formula.

First, let's find the midpoint of the line segment. The midpoint formula is given by: [ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ]

Given one endpoint at (3, 2), let's denote the coordinates of the other endpoint as (x, y). We know that the midpoint is on the line (2y + 9x = 3), so we can use this information to find the other endpoint.

Using the midpoint formula and substituting the midpoint into the equation of the line, we get: [ \frac{3 + x}{2} = \frac{2 + y}{2} ] [ 3 + x = 2 + y ] [ y = x + 1 ]

Now, substitute ( y = x + 1 ) into the equation of the line (2y + 9x = 3) to solve for x: [ 2(x + 1) + 9x = 3 ] [ 2x + 2 + 9x = 3 ] [ 11x = 1 ] [ x = \frac{1}{11} ]

Now that we have the x-coordinate, we can find the y-coordinate using ( y = x + 1 ): [ y = \frac{1}{11} + 1 ] [ y = \frac{12}{11} ]

Therefore, the other end of the line segment is at the point ( \left( \frac{1}{11}, \frac{12}{11} \right) ).

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.

- A line segment is bisected by a line with the equation # 4 y - 3 x = 2 #. If one end of the line segment is at #( 2 , 1 )#, where is the other end?
- Draw a line #l# and two points A and B not lying on l. Make sure that the line #bar(AB)# is not perpendicular to #l#. Find the point C on #l# such that AC = BC?
- A triangle has corners A, B, and C located at #(4 ,8 )#, #(7 ,4 )#, and #(5 ,3 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A triangle has corners A, B, and C located at #(3 ,5 )#, #(2 ,1 )#, and #(5 , 8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A line segment is bisected by a line with the equation # 2 y - 2 x = 2 #. If one end of the line segment is at #( 3 , 8 )#, where is the other end?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7