Question

The points (3, 9), (4, 8) and (5, 7) are _____

• A. Vertices of an equilateral triangle
• B. Vertices of a right angled triangle
• C. Vertices of a isosceles triangle
• D. None of the above

Answer 1

The correct option is D

None of the above

A = (3, 9)

B = (4, 8)

C = (5, 7)

AB = $\sqrt{(4-3{)}^2+(8-9{)}^2}=\sqrt{1+1}=\sqrt{2}$

BC = $\sqrt{(5-4{)}^2+(7-8{)}^2}=\sqrt{1+1}=\sqrt{2}$

CA = $\sqrt{(3-5{)}^2+(9-7{)}^2}=\sqrt{4+4}=2\sqrt{2}$

So, we observe that sides AB and BC are equal AB = BC =$\sqrt{2}$ and side AC = $2\sqrt{2}$

When two sides of any triangle is equal, if forms an isosceles triangle.

Is these points are the vertices of isosceles triangle?

Think about it!!

No. why?

First thing, we should look whether these three points can form any type of triangle.

Necessary condition for any triangle is sum of two sides should be greater than third side of triangle.

Here, sum of AB + BC = CA.

This is NOT sufficient to construct a triangle.

So, we cannot draw any type of triangle with these three points. Correct answer is option D.