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)
What is the following system
Answer:
Hi there!
The answer to this question is: 6x+3
Step-by-step explanation:
Step 1: combine alike terms
in the equation there are two numbers that end with x: 8x and -2x
you simply add them together to get 6x
Step 2: combine numbers
in this equations there are two numbers: 7 and -4
you simply add them together to get 3
Then your final answer should be 6x+3
Answer:
d
Step-by-step explanation:
because both the measurement and the congruent side are opposite in sentence
