Use cross products to find the area of the triangle in the xy-plane defined by (1, 2), (3, 4), and (−7, 7).

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)

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

560

step-by-step explanation:

giggidy