Find the slope of the line through (4, 1) and (5, 3), then interpret it?
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Consider the attached figure. The whole rectangle is ABCD, while AEGF is the part located in the third quadrant. In fact, this quadrant is composed by all the points with both coordinates negative.
To answer the question, let's compute the area of the two rectangles and see what part of ABCD is AEGF.
A and B have the same x coordinate, so the length of AB is given by the absolute difference of their y coordinates:
Similarly, but exchanging the role of x and y, we compute the length of BC:
So, the area of the rectangle is
The same procedure allows us to compute width and height of the sub-rectangle in the third quadrant:
So, the area of the portion located in the third quadrant is
This means that the ratio between the two area is
If we want this ratio to be a percentage, just make sure that the denominator is 100:
