Question

Which type of triangle is formed with the points A(1, 7), B(-2, 2), and C(4, 2) as its vertices?

Answer 1

A(-1,2,3), B(-1,3,5), C(0,-1,1)

AB=OB-OA
AB=(-1,3,5) - (-1,2,3)
AB= (0,1,2)

AC=OC-0A
AC=(0,-1,1) - (-1,2,3)
AC=(1,-3,-2)

Using the scalar product
cosx= (AB. AC)/(|AB| |AC|)
cosx=(0,1,2) . (1,-3,2)/ sqrt(0^2 +1^2 +2^2) sqrt(1^2+3^2+2^2)
x=83.1 degrees



|A| = sqrt14

|B| = sqrt35

A=1/2 ab sinC

A= 1/2(sqrt14sqrt35)sin83.1
A= 10.99 units^2