Y=-5x+3 in standard form
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Answer:
or 1.9099
Step-by-step explanation:
Look for y values at each of those given values of "x" and apply the slope formula. When x = pi. y = -1 so the coordinate is . When x = 3pi/2, y = 2 so the coordinate is
Plug those values into the slope formula:
You need a common denominator of pi:
Do the math on that to get a slope of
I love these. It's often called the Shoelace Formula. It actually works for the area of any 2D polygon.
We can derive it by first imagining our triangle in the first quadrant, one vertex at the origin, one at (a,b), one at (c,d), with (0,0),(a,b),(c,d) in counterclockwise order.
Our triangle is inscribed in the rectangle. There are three right triangles in that rectangle that aren't part of our triangle. When we subtract the area of the right triangles from the area of the rectangle we're left with the area S of our triangle.
That's the cross product in the purest form. When we're away from the origin, a arbitrary triangle with vertices will have the same area as one whose vertex C is translated to the origin.
We set
That's a perfectly useful formula right there. But it's usually multiplied out:
That's the usual form, the sum of cross products. Let's line up our numbers to make it easier.
(1, 2), (3, 4), (−7, 7)
(−7, 7),(1, 2), (3, 4),
[tex]A = \frac 1 2 ( 1(7)-2(-7) + 3(2)-4(1) + -7(4) - (7)(3)
