The coordinates R(1, -3), S(3, -1) T(5,-7) form what type of polygon?a right trianglean acute trianglean equilateral trianglean obtuse triangle

Accepted Solution

Answer:A right triangleStep-by-step explanation:Suppose a, b, c are the sides of a triangle,If a² = b² + c² or b² = a² + c² or c² = a² + b²Then the triangle is called a right angled triangle,If a² + b² > c², a² + c² > b², b² + c² > a²Then the triangle is called an acute triangle,If a = b = cThen 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,[tex]RS=\sqrt{(3-1)^2+(-1-(-3))^2}=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{8}\text{ unit }[/tex]Similarly,ST = √40 unit,TR = √32 units,Since, ST² = RS² + TR²Hence, by the above explanation it is clear that,Triangle RST is a right angled triangle,First option is correct.