Question

Using distance formula,show that the points A(3,1), B(6,4) and C(8,6) are collinear

Answer 1

Answer:

Here's the proof..

Step-by-step explanation:

Answer 2

Answer:  The proof is given below.

Step-by-step explanation:  We are given to show that the points A(3,1), B(6,4) and C(8,6) are collinear using distance formula.

Distance formula :  The distance between the points (a, b) and (c, d) is given by

$D=\sqrt{(c-a)^2+(d-b)^2}.$

We know that

any three points P, Q and R are collinear if PQ + QR = PR.

Now, the lengths AB, BC and AC can be calculated using distance formula as follows :

$AB=\sqrt{(6-3)^2+(4-1)^2}=\sqrt{9+9}=\sqrt{18}=3\sqrt{2},\\\\\\BC=\sqrt{(8-6)^2+(6-4)^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt2,\\\\\\AC=\sqrt{(8-3)^2+(6-1)^2}=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}.$

We note that

$3\sqrt5+2\sqrt=5\sqrt5\\\\\Rightarrow AB+BC=AC.$

Thus, the points A, B and C are collinear.

Hence proved.