Question

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

a right triangle
an acute triangle
an equilateral triangle
an obtuse triangle

Answer 1

this isa right triangle!!!

Explanation:

this isa right triangle!!!

Answer 2

A right triangle

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=√((3-1)^2+(-1-(-3))^2)=√(2^2+2^2)=√(4+4)=√(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.