A line segment is bisected by a line with the equation # - 3 y + 6 x = 6 #. If one end of the line segment is at #( 3 , 3 )#, where is the other end?
The other end could be any point on the line
For convenience, I will rearrange the given equation Consider the vertical line through The distance between The point Therefore Therefore one possible endpoint would be at
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Perhaps less obviously, any point on a line through
as
Since
this vertical line will intersect
will also be a line segment endpoint bisected by the given equation.
Which can be simplified as
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To find the other end of the line segment, you can solve the given equation for y to obtain the equation of the line segment. Then, substitute the x-coordinate of the given point into the equation to find the corresponding y-coordinate.
First, solve the equation -3y + 6x = 6 for y: -3y = -6x + 6 y = 2x - 2
Next, substitute the x-coordinate of the given point (3, 3) into the equation: y = 2(3) - 2 y = 6 - 2 y = 4
So, the other end of the line segment is at the point (3, 4).
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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.
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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- How do you write the equation of the perpendicular bisector of the segment with the given endpoints #(2,5)# and #(4,9)#?
- A triangle has corners A, B, and C located at #(2 ,7 )#, #(1 ,4 )#, and #(6 , 3 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- What is the orthocenter of a triangle with corners at #(1 ,3 )#, #(6 ,9 )#, and (2 ,4 )#?

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