Show that the points (-5,1),(1,-1) and (4,-2) are collinear

1.	Show that the points (-5,1),(1,-1) and (4,-2) are collinear
Answer» POINTS GIVEN: (-5,1); (1,-1); (4,-2) x1 = -5 x2 = 1 x3 = 4 y1 = 1 y2 = -1 y3 = -2 For the points to be collinear :- x₁(y₂ -y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) = 0 Thus, LHS = x₁(y₂ -y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) = -5(-1+2) + 1(-2-1) + 4(1+1) = -5 + -3 + 8 = -5 + 5 =0 Therefore, LHS=RHS

Answer»

POINTS GIVEN: (-5,1); (1,-1); (4,-2)

x1 = -5

x2 = 1

x3 = 4

y1 = 1

y2 = -1

y3 = -2

For the points to be collinear :-

x₁(y₂ -y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) = 0

Thus, LHS = x₁(y₂ -y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)

= -5(-1+2) + 1(-2-1) + 4(1+1)

= -5 + -3 + 8

= -5 + 5

Therefore, LHS=RHS

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