Question

Show that the origin is with in the triangle whose angular point are (2,1),(3,_2),and (_4,1)?

Answer 1

Answer:

origin is with in the triangle

Step-by-step explanation:

Show that the origin is with in the triangle whose angular points are (2,1) , (3,-2) , and (-4,-1).

Let say  A = (2,1)  B = (3 , -2)  & C = (-4,-1)

Origin = (0,0)

if origin lies with in Triangle ABC

then Area of ΔABC = Area of ΔOAB +  Area of ΔOAC + Area of ΔOBC

Area of Triangle using formula [ x1(y2 – y3) + x2(y3 – y1) + x3(y1-y2)]/2

A = (2,1)  B = (3 , -2)  & C = (-4,-1)

Area of ΔABC  = [2(-2 -(-1)) + 3(-1 - 1) + (-4)(1 -(-2))]/2 = [-2 -6 -12]/2 = 10

O=(0,0) A = (2,1)  B = (3 , -2)

Area of ΔOAB = [0(1- (-2)) + 2(-2 - 0) +3(0-1)}/2 =[-4 -3]/2 = 7/2

O=(0,0) A = (2,1) C = (-4 , -1)

Area of ΔOAC = [0(1- (-1)) + 2(-1 - 0) +(-4)(0-1)}/2 =[-2+4]/2 = 1

O=(0,0) B = (3,-2) C = (-4 , -1)

Area of ΔOBC = [0(-2- (-1)) + 3(-1 - 0) +(-4)(0-(-2))}/2 =[-3-8]/2 = 11/2

Area of ΔOAB +  Area of ΔOAC + Area of ΔOBC = 7/2 + 1 + 11/2 = 20/2 = 10 = Area of ΔABC

=>  Area of ΔABC = Area of ΔOAB +  Area of ΔOAC + Area of ΔOBC

Hence origin is with in the triangle