Question

Determine if triangle ABC with coordinates A(0, 2), B(2, 5), and C(−1, 7) is an isosceles triangle. Use evidence to support your claim. Please

help its long answer

Answer 1

Triangle ABC is isosceles.

Explanation:

An isosceles triangle means two sides of the triangle should be equal.

Given vertices of the triangle are A(0, 2), B(2, 5) and C(-1, 7)

We will use the formula to find the length

`=√((x-x')^2+(y+y')^2)`

Now length AB =
`√((0-2)^2+(2-5)^2)`

=
`√(2^2+3^2)`

=
`√(4+9)`

=
`√(13)`

Length AV =
`√((0+1)^2+(2-7)^2)`

=
`√(1^2+(-5)^2)`

=
`√(1+25)`

=
`√(26)`

Length BC =
`√((2+1)^2+(5-7)^2)`

=
`√(3^2+2^2)`

=
`√(9+4)`

=
`√(13)`

mAB = mBC =
`√(13)`,

Therefore, triangle ABC is isosceles.