The explanation for this is one of my favorite pieces of mathematical reasoning. First, let's thing about distance; what's the shortest distance between two points? <em>A straight line</em>. If we just drew a straight line between A and B, though, we'd be missing a crucial element of the original problem: we also need to pass through a point on the line (the "river"). Here's where the mathemagic comes in.
If we take the point B and <em>reflect it over the line</em>, creating the point B' (see picture 1), we can draw a line straight from A to B' that passes through a point on the line. Notice the symmetry here; the distance from the intersection point to B' is<em> the same as its distance to B</em>. So, if we reflect that segment back up, we'll have a path to B, and because it came from of the line segment AB', we know that it's <em>the shortest possible distance that includes a point on the line</em>.
If we apply this same process to our picture, we see that the line segment AB' crosses the line
at the point (1, 1)
Answer:
g = 23/16
Step-by-step explanation:
3/16 = (-5/4) + g
Add 5/4 on both sides.
3/16 + 5/4 = g
Make denominators equal and add.
3/16 + 20/16 = g
23/16 = g
Answer:
y = 5x + 15
Step-by-step explanation:
the y intercept is 15 because that is the about that will initially be paid no matter how much or how little you swim, and the slope is five because the amount paid in all is determined by how much he swims. hope this helps :)