Question

Show that the points are collinear 2,3 1,4 and -3,8.

Answer 1

Given ;

• A(2,3)
• B(1,4)
• C(-3,8)

To prove : these points are collinear.

Thus ar(∆ABC) should be= 0

By using ar of ∆ formula;

LHS:

$\frac{1}{2} |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| = 0$

then ;

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

• LHS =
• 2(4-8) + 1(8-3) -3(3-4)
• 2(-4) + 1(5) -3(-1)
• -8 + 5 + 3
• -8 + 8 = 0
• = RHS

since the area of ∆ABC = 0

Thus points •A •B & •C are collinear.

#answerwithquality

#BAL