Question

The coordinates R(1, -3), S(3, -1) T(5,-7) form what type of polygon?

Answer 1

- It's an obtuse triangle.

Answer 2

Answer:

A right triangle

Step-by-step explanation:

Suppose a, b, c are the sides of a triangle,

If a² = b² + c² or b² = a² + c² or c² = a² + b²

Then the triangle is called a right angled triangle,

If a² + b² > c², a² + c² > b², b² + c² > a²

Then the triangle is called an acute triangle,

If a = b = c

Then the triangle is called an equilateral triangle,

If a² + b² < c², where c is the largest side of the triangle,

Then the triangle is called an obtuse triangle,

Now, In triangle RST,

By the distance formula,

$RS=\sqrt{(3-1)^2+(-1-(-3))^2}=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{8}\text{ unit }$

Similarly,

ST = √40 unit,

TR = √32 units,

Since, ST² = RS² + TR²

Hence, by the above explanation it is clear that,

Triangle RST is a right angled triangle,

First option is correct.