Respuesta :
we know that
An equilateral truangle has three equal length sides
so
If triangle ABC is an equilateral triangle
then
AB=BC=AC
so
step 1
Find out the distance AB
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^2+(x2-x1)^2}[/tex]we have
A (-4,6)
B (6,6)
substitue in the formula
[tex]\begin{gathered} d=\sqrt{(6-6)^2+(6+4)^2} \\ d=\sqrt{(0)^2+(10)^2} \\ dAB=10\text{ units} \end{gathered}[/tex]step 2
Find the distance BC
we have
B (6,6)
C( 1,-3)
substitute the values in the formula
[tex]\begin{gathered} d=\sqrt{(-3-6)^2+(1-6)^2} \\ d=\sqrt{(-9)^2+(-5)^2} \\ d=\sqrt{81+25} \\ dBC=\sqrt{106\text{ units}} \end{gathered}[/tex]we have that
AB is not equal to BC
therefore
Is not an equilateral triangle
Is not necessary calculate the distance AC
