1. ## 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 $-\frac {1}{2}$)

2. Originally Posted by dannyc
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.

Follow?

3. 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?)

4. 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.

5. Originally Posted by pickslides
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.