# A line segment is bisected by a line with the equation # -3 y + 7 x = 1 #. If one end of the line segment is at #(9 ,2 )#, where is the other end?

The point

In slope-intercept form, write the given equation for the bisector line:

Subtract equation [2] from equation [1] to obtain the x coordinate of the point of intersection.

There will be two changes to the x coordinate for the other end:

Enter the x coordinate into equation [2] to determine the y coordinate of the other end.

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To find the other end of the line segment bisected by the line with the equation -3y + 7x = 1, first find the midpoint of the given segment. Then, use the midpoint formula to determine the coordinates of the other end.

The midpoint formula is: [ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) ]

Given point A(9, 2) is one end of the line segment. Let's denote the coordinates of the other end as (x, y).

Substitute the coordinates of point A and solve for the unknown point: [ 9 + x = 2 ] [ 2 + y = 2 ]

Solve these equations to find the values of x and y.

[ x = -7 ] [ y = 0 ]

Therefore, the other end of the line segment is at (-7, 0).

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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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