Question

Find the area of triangle PQR if P is (3,18),Q(-5,7) and R is (13,1). Please Explain how you got the answer

Answer 1

Two Options:
There is a formula from coordinate geometry, but it is difficult to remember (I can show you if you want), or we would need to find the side lengths using distance formula, then use the law of cosines to find an angle, then we can use a simple formula from trigonometry to find the area.

Answer 2

okk

Answer 3

show me please

Answer 4

The formula is quicker than the second method.
\[Area=\frac{1}{2}|P _{x}(Q _{y}-R _{y})+Q _{x}(R _{y}-P_{y})R_{x}(P_{y}-Q_{y})|\]where Px is the x-coordinate of point P, Qy=the y-coordinate of point Q, etc.

For your triangle,\[Area=\frac{1}{2}|3(7-1)+(-5)(1-18)+13(18-7)|=123\]