Question

Find the area of the triangle defined by the coordinates (7,1), (0,10), and (9,4). (To the nearest tenth).

Answer 1

Answer:

$\boxed{Area=19.5units^2}$

Step-by-step explanation:

A triangle is any polygon with exactly 3 sides. Let's call this sides the vertices of the triangle, and let's say:

$(7,1)=A(7,1) \\ \\ (0,10)=B(0,10) \\ \\ (9,4)=C(9,4)$

Where:

$A=(A_{x},A_{y}) \\ B=(B_{x},B_{y}) \\ C=(C_{x},C_{y})$

A formula for finding the area of a triangle given its vertices is:

$Area=|\frac{A_{x}(B_{y}-C_{y})+B_{x}(C_{y}-A_{y})+C_{x}(A_{y}-B_{y})}{2}| \\ \\ Area=|\frac{7(10-4)+0(4-1)+9(1-10)}{2}| \\ \\ Area=|\frac{-39}{2}| \\ \\ \boxed{Area=19.5units^2}$

Finally, the area of the triangle defined by the coordinates (7,1), (0,10), and (9,4), to the nearest tenth is 19.5 squared units.