Thread: finding slope

Given that triangle has points, and , point can be moved along a certain line with points and remaining stationary, and the area of Δ will not change. What is the slope of that line?

(It says the answer in my book which is )

Originally Posted by dannyc

Given that triangle has points, and , point C can be moved along a certain line with points A and B remaining stationary, and the area of Δ will not change. What is the slope of that line?

(It says the answer in my book which is )

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?

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?)

Area of a rectangle is always

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.

Originally Posted by pickslides

Area of a rectangle is always

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.