Question

Show that the points A( - 6, 10 ) , B( - 4, 6 ) and C( 3, -8 ) are collinear. Find ratio between AB and AC.

Answer 1

Answer:

2:9

Step-by-step explanation:

Distance formula D = √(x₂ - x₁)² + (y₂ - y₁)²

Given: A(-6,10),B(-4,6) and C(3,-8)

⇒ AB = √(-4 + 6)² + (6 - 10)²

         = √(2)² + (-4)²

         = √20.

         = 2√5

⇒ BC = √(3 + 4)² + (-8 - 6)²

         = √(7)² + (-14)²

         = √245

         = 7√5

⇒ AC = √(3 + 6)² + (-8 - 10)²

         = √(9)² + (-18)²

         = √405

        = 9√5

Now, AB + BC = 2√5 + 7√5 = 9√5 = AC.

Therefore,the points are collinear.

Also, AB : AC = 2√5/9√5

                      = 2/9

                      = 2:9

Therefore, ratio between AB and AC = 2:9.

Hope it helps!

Answer 2

Answer:

2:9

Step-by-step explanation:

Given: A(-6,10),B(-4,6) and C(3,-8)

⇒ AB = √(-4 + 6)² + (6 - 10)²

= √(2)² + (-4)²

= √20.

= 2√5

⇒ BC = √(3 + 4)² + (-8 - 6)²

= √(7)² + (-14)²

= √245

= 7√5

⇒ AC = √(3 + 6)² + (-8 - 10)²

= √(9)² + (-18)²

= √405

= 9√5

Now, AB + BC = 2√5 + 7√5 = 9√5 = AC.

Therefore,the points are collinear.

Also, AB : AC = 2√5/9√5

= 2/9

= 2:9

Therefore, ratio between AB and AC = 2:9.