Geometry chap 5: #4 - What are the equations for the 4 lines

[Guest]

What are the equations for the 4 lines that form the boundaries of the shaded area in the figure shown?

Points are:

(4,0) - (4,2) - (4,0)

The answer yielded a slope of -1/2 but I came to a slope of -2 because I inverted the points within the formula. So I guess my question is; is there a logic when picking points to plug in as:

y1-y2/x1-x2

Please let me know if the question makes any sense or requires clarification.

[rfernandez]

Actually, the points that bound the shaded region are: (0,0), (0,4), (4,2), and (4,0).

I think your question is how to apply the slope formula (y2 - y1)/(x2 - x1) to determine the slope of the line that contains the points (0,4) and (4,2).

There are two ways to plug in the values, and both ways yield the same answer:

(x1,y1) = (4,2) and (x2,y2) = (0,4)
(4-2)/(0-4) = 2/-4 = -1/2

or
(x1,y1) = (0,4) and (x2,y2) = (4,2)
(2-4)/(4-0) = -2/4 = -1/2

[Guest]

Thanks...so if I understand this correctly, no matter how you plug in the points given into the slope formula, it should yield the same answer. If it doesn't, I probably made a minor math error?

Thanks again.

[StaceyKoprince]

yep - as long as you're using the same 2 points, and as long as you assign them consistently (first point is always the first point, second point is always the second point), you should get the same slope!