Problema Solution

the vertices of a right triangle are A(3,3), B(-4,4), C(1,-5). Find the area of the triangle.

Answer provided by our tutors

Area of a triangle with vertices (x1,y1),(x2,y2),(x3,y3) is calculated by the formula:

A = (1/2)[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]

In our case we have:

(x1, y1) = (3, 3), that is x1 = 3, y1 = 3

(x2, y2) = (-4, 4), that is x2 = -4, y2 = 4

(x3, y3) = (1, -5), that is x3 = 1, y3 = -5

Plug in the values into the formula:

A = (1/2)[3(4−(-5))+(-4)((-5)−3)+1*(3−4)]

A = 29

The area of the triangle is 29.