Khan academy what is the area of the triangle with vertices (0,0),(-3,5),(2,-7)

Since you have the coordinates of the three vertices, the most straightforward method is to calculate the length of the sides using the distance formula
d(P_1,P_2)=SQRT((X_1-X_2)^2+(Y_1-Y_2)^2)
where SQRT is the square root function, X_1, Y_1) are the coordinates of point P_1, etc.
With the three lengths available, use Heron's (sometimes called Hero's) to find the area.
Here is Heron's formula.
Let's call the lengths a, b, and c
Let p be the semi-perimeter p= (a+b+c)/2
Then
Area= SQRT [ p(p-a)(p-b)(p-c) ]
Make sure that there is a matching ) parenthesis to the one in the SQRT.

Alternatively,
You can choose the base as the side opposite the vertex (0,0)
Calculate the equation of the line that supports the base.
Calculate the equation of the line issuing from (0,0) and perpendicular t the base.
Calculate the coordinates of the intersection point , call it H, of the base and its perpendicular line (coming from (0,0)).
Calculate the distance OH, that is the height relative to the chosen base.
Use the formula Area= base*height/2

Now it is up to you to choose one of the two methods and calculate the area of that triangle. The second method involves more calculations than the first, and more possibilities of errors. Good Luck