# A line segment is bisected by a line with the equation # 5 y -4 x = 1 #. If one end of the line segment is at #(3 ,4 )#, where is the other end?

The other end is

Let's rewrite the line's equation.

The incline is

The segment's equation is

The location where the lines converge

Then,

and

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To find the other end of the line segment bisected by the line (5y - 4x = 1), we need to find the point of intersection between this line and the line segment. First, we'll determine the equation of the line segment using the given endpoint ((3, 4)) and the midpoint formula.

The midpoint formula states that the midpoint of a line segment with endpoints ((x_1, y_1)) and ((x_2, y_2)) is ((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})).

Given one endpoint ((3, 4)) and assuming the other endpoint is ((x, y)), we find the midpoint.

Midpoint: ((\frac{3 + x}{2}, \frac{4 + y}{2}))

Now, since the line (5y - 4x = 1) bisects the line segment, the midpoint lies on it. Thus, we'll equate the coordinates of the midpoint to the equation of the line.

Equating the coordinates of the midpoint to the equation of the line, we have:

[\frac{3 + x}{2} = \frac{1}{4}(4x + 1)] [\frac{4 + y}{2} = \frac{1}{5}(5y - 1)]

Now, solve these equations to find (x) and (y). Once you have (x) and (y), you'll have the coordinates of the other end of the line segment.

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The other end of the line segment is at the point (7, 2).

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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.

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- What is the orthocenter of a triangle with corners at #(1 ,2 )#, #(5 ,6 )#, and (4 ,6 )#?
- A line segment is bisected by a line with the equation # - y + 7 x = 1 #. If one end of the line segment is at #( 7 , 2 )#, where is the other end?
- Given 2 numbers #(a,b)# it is possible to perform geometrically the following algebraic operations: a+b, a−b, a*b, a/b. Use only a straight edge and compass to show each operation?

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