Question

The triangle with the vertices (-2,4), (0,0) and (5,-1) is_________. a)right angled b) obtuse angled triangle c) acute angled triangle d) equilateral triangle​

Answer 1

Answer:

I think its acute angled triangle

Answer 2

Answer:

This is a (b)obtuse-angled triangle.

Step-by-step explanation:

Let, the triangle has the vertices A(-2,4), B(0,0), and C(5,-1)

So, the side AB;

$AB = \sqrt{ {(0 - ( - 2))}^{2} + {(0 - 4)}^{2} } \\ = \sqrt{20 } \: unit$

the side BC ;

$B C= \sqrt{ {(5 - 0)}^{2} + {(( - 1) - 0)}^{2} } \\ = \sqrt{26 } \: unit$

the side AC;

$AC= \sqrt{ {(5 - ( - 2))}^{2} + {(( - 1) - 4)}^{2} } \\ = \sqrt{74 } \: unit$

So, we get this can't be a right angled as the sum of squares of AB and BC is not equal to AC

This is not a equilateral triangle also as AB, BC, and AC are not same

This is not a Acute angled triangle also as

AC>> AB ≈ BC

A triangle whose any one of the angles is an obtuse angle or more than 90°, then it is called an obtuse-angled triangle or obtuse triangle.

So this is a obtuse-angled triangle.