Answer:
This is an acute, scalene triangle.
Step-by-step explanation:
Alright, to find the type of triangle, let's use the distance formula (to find the length of the sides).
d = [tex]\sqrt{(x_2-x_1)+(y_2-y_1)}[/tex]
The distance from (2,3) to (5,0) is [tex]3\sqrt{2}[/tex]. = 4.24264068
The distance from (2,3) to (4,4) is [tex]\sqrt{5}[/tex]. = 2.23606797
The distance from (5,0) to (4,4) is [tex]\sqrt{17}[/tex] . = 4.12310562
The length that is longest is [tex]3\sqrt{2}[/tex].
Let's label it c.
Let's label the distance from (2,3) to (4,4) a.
Let's label the distance from (5,0) to (4,4) b.
If c^2 = a^2+b^2, this is a right triangle.
If c^2 < a^2+b^2, this is an acute triangle.
If c^2> a^2+b^2, this is an obtuse triangle.
( [tex]3\sqrt{2}[/tex])^2 vs.( [tex]\sqrt{5}[/tex] )^2 +( [tex]\sqrt{17}[/tex])^2
18 vs. 5+ 17
18 vs 22.
c^2 < a^2 + b^2.
This is an acute triangle.
None of the sides are equal, so this is a scalene triangle.
This is an acute, scalene triangle.
