# A line segment is bisected by a line with the equation # 4 y - 6 x = 8 #. If one end of the line segment is at #( 1 , 8 )#, where is the other end?

Then:

The midpoint's coordinates are provided by:

So:

Hence:

and

Thus, an additional endpoint is:

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To find the other end of the line segment bisected by the line (4y - 6x = 8), we first need to determine the coordinates of the midpoint of the line segment.

The midpoint formula is:

[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ]

Given one end of the line segment as (1, 8), we'll use this point along with the midpoint formula to find the midpoint.

Substituting the given point (1, 8) into the midpoint formula:

[ x_1 = 1, \ y_1 = 8 ]

We don't have the coordinates of the other end, so we denote them as (x, y). Now we have:

[ \frac{1 + x}{2} = x ] [ \frac{8 + y}{2} = y ]

We can simplify these equations:

[ 1 + x = 2x ] [ 8 + y = 2y ]

Rearranging terms:

[ x = 1 ] [ y = 8 ]

Now we have found the coordinates of the midpoint of the line segment, which is (1, 8). Since the line segment is bisected, the other end of the line segment will also have the same coordinates as the midpoint. Therefore, the other end of the line segment is also at (1, 8).

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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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