Question

triangle ABC has the following verticles A (-4,6)B (6,6)C( 1,-3) is triangle ABC an equilateral traingle and why?

Answer 1

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

`d=√((y2-y1)^2+(x2-x1)^2)`

we have

A (-4,6)

B (6,6)

substitue in the formula

`\begin{gathered} d=√((6-6)^2+(6+4)^2) \\ d=√((0)^2+(10)^2) \\ dAB=10\text{ units} \end{gathered}`

step 2

Find the distance BC

we have

B (6,6)

C( 1,-3)

substitute the values in the formula

`\begin{gathered} d=√((-3-6)^2+(1-6)^2) \\ d=√((-9)^2+(-5)^2) \\ d=√(81+25) \\ dBC=\sqrt{106\text{ units}} \end{gathered}`

we have that

AB is not equal to BC

therefore

Is not an equilateral triangle

Is not necessary calculate the distance AC