Question

15. By what condition due to the points A(1, 1), B(-2, 7) and C(3,-3) are collinear.​

Answer 1

Answer:

A (1, 1)

B (-2, 7)

C (3, -3)

Slope of AB =

−2−1

7−1

=

−3

6

=−2

Slope of BC =

−2−3

7−(−3)

=

−5

10

=−2

Slope of AC =

1−3

1−(−3)

=

−2

4

=−2

Since slope of AB = Slope of BC = Slope of AC

Hence, points A,B,C are collinear

Answer 2

Answer:

The condition is that, BC = AB + CA, A, B and C are colinear and A is lying in between B and C.

Step-by-step explanation:

A(1,1), B(-2,7) and C(3,-3)

AB $=\sqrt{[1-(-2)]^2 + [1-7]^2]} = \sqrt{9 + 36} = \sqrt{45} =3\sqrt{5}$

BC $=\sqrt{[-2-3]^2 + [7-(-3)]^2]} = \sqrt{25 + 100} = \sqrt{125} =5\sqrt{5}$

CA $=\sqrt{[3-1]^2 + [-3-1]^2]} = \sqrt{4 + 16} = \sqrt{20} =2\sqrt{5}$

The condition is that, BC = AB + CA, A, B and C are colinear and A is lying in between B and C.