Question

2.
Determine whether the given points are collinear.
(1) A(0,2), B(1,-0.5), C(2,-3)
(2) P(1, 2), Q(2, 8/5), R(3, 6/5)

Solve using distance formula​

Answer 1

In the first one points will be collinear if AB+BC= AC and similarly PQ+QR= PR in the second part.

The distance formula= ✓(x2-x1)²+(y2-y1)²

i. AB= ✓(x2-x1)²+(y2-y1)²

= ✓(1-0)²+(-0.5-2)²

= ✓1²+(-2.5)²

=✓1+6.25

=✓7.25

BC= ✓(x2-x1)²+(y2-y1)²

= ✓(2-1)²+(-3-(-0.5) )²

=✓(1)²+(-3+0.5)²

=✓1+(-2.5)²

=✓1+6.25

=✓7.25

AC= ✓(x2-x1)²+(y2-y1)²

= ✓(2-0)²+(-3-2)²

= ✓2²+(-5)²

= ✓4+25

= ✓29

When you add AB and BC you will find it is equal to AC. Therefore the points A,B and C are collinear.

Similarly do the second one.

Hope this helps...