Question

Show that the points (3,2),(4,5/2) and (5,3) are collinear by distance formula

Answer 1

Given:

A = (3,2)

B = (4,5/2)

C = (5,3)

To find:

Show that the points are collinear by distance formula.

Solution:

$AB = \sqrt{(4 - 3)^{2} +(5/2 - 2)^{2} }\\\\AB = \sqrt{(1)^{2} + (1/2)^{2} } \\\\AB = \sqrt{1 + 1/4}\\\\AB=\sqrt{5/4}\\\\AB = \sqrt{5} / 2$

So, AB = √5 / 2

$BC = \sqrt{(5 - 4)^{2} +(3 - 5/2)^{2} }\\\\BC = \sqrt{(1)^{2} +(1/2)^{2} } \\\\BC = \sqrt{1 + 1/4}\\\\BC = \sqrt{5/4} \\\\BC = \sqrt{5} / 2$

So, BC = √5 / 2

$CA = \sqrt{(5-3)^{2} + (3 - 2)^{2} }\\\\CA = \sqrt{(2)^{2} + (1)^{2} }\\\\CA = \sqrt{4 + 1}\\\\CA = \sqrt{5}$

So, CA = √5

AB + BC = CA

√5/2 + √5/2 = √5

As AB + BC = CA

Therefore, (3,2), (4,5/2) and (5,3) are collinear.

Answer 2

Step-by-step explanation:

Find the following attachment.

Hope it helps....