Question

I need help finding out if this triangle is isosceles, scalene or equilateral

Answer 1

We will determine it as follows:

*We can see that the triangle has the following vertex:

A(1, 3)

B(3, 7)

C(5, 3)

Now, we determine the directional segments:

$AB=(3-1,7-3)\Rightarrow AB=(2,4)$$AC=(5-1,3-3)\Rightarrow AC=(4,0)$$BC=(5-3,3-7)\Rightarrow BC=(2,-4)$

Now, we determine the distance of each segment:

$d_{AB}=\sqrt[]{2^2+4^2}\Rightarrow d_{AB}=2\sqrt[]{5}$$d_{AC}=\sqrt[]{4^2+0^2}\Rightarrow d_{AC}=4$$d_{BC}=\sqrt[]{2^2+(-4)^2}\Rightarrow d_{BC}=2\sqrt[]{5}$

From this, we have that the triangle is isosceles.