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Math Help - finding slope

  1. #1
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    finding slope

    Given that triangle ABC has points, A(8,2), B(0,6), and  C(-3,2), point C can be moved along a certain line with points A and B remaining stationary, and the area of Δ ABC will not change. What is the slope of that line?

    (It says the answer in my book which is -\frac {1}{2})
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  2. #2
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    Quote Originally Posted by dannyc View Post
    Given that triangle ABC has points, A(8,2), B(0,6), and  C(-3,2), point C can be moved along a certain line with points A and B remaining stationary, and the area of Δ ABC will not change. What is the slope of that line?

    (It says the answer in my book which is -\frac {1}{2})
    The line you are after is parallel to AB so all you need to do is find the gradient of the line between A and B.

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  3. #3
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    Yep--it comes out to the right slope. But what's the logic behind it? (Why is the correct line parallel, is there a mini proof or is it more common knowledge that I somehow missed?)
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  4. #4
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    Area of a rectangle is always \frac{1}{2}\times \text{base}\times \text{height}

    The base and height will only always be the same (so the area is constant) for C, if C itself is only moving parallel to the line AB.

    Draw a picture of ABC and move C around parallel to AB, you will see the base and height are always the same.
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  5. #5
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    Quote Originally Posted by pickslides View Post
    Area of a rectangle is always \frac{1}{2}\times \text{base}\times \text{height}
    The area of a triangle, of course.

    The base and height will only always be the same (so the area is constant) for C, if C itself is only moving parallel to the line AB.

    Draw a picture of ABC and move C around parallel to AB, you will see the base and height are always the same.
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