Question

show that points are collinear by area concept (-5,7)(-4,5)(1,-5).​

Answer 1

Step-by-step explanation:

Let A = (-5,7)

B = (-4,5)

C = (1,-5)

We know that if the area of triangle is equal to zero then these point are collinear

So, we have to prove that ar(∆ABC) = 0 square units

Area of ∆ =

1/2[x¹(y²-y³) + x²(y³-y¹) + x³(y¹-y²)]

putting values of x¹,x²,x³,y¹,y²,y³ in this

1/2[-5(5+5) + (-4)(-5-7) + 1(7-5) ]

1/2[-5×10 + (-4×-12) + 1×2 ]

1/2[-50 + 48 + 2]

1/2[-50 + 50]

1/2×0

0

ar(∆ABC) = 0

hence these points are collinear

hope my answer will help you better