Question

determine if the points 5,-2, 6,4, 7,-2 are collinear​

Answer 1

Answer:

5 -2) (6 4) and (7 -2) are the vertices of an isosceles triangle

Step-by-step explanation:

Let Say

A ( 5 , -2)

B (6 , 4)

C ( 7 , -2)

Length of each sides

AB =\sqrt{(6-5)^2 + (4 -(-2))^2} = \sqrt{1^2 + 6^2} = \sqrt{1 + 36} = \sqrt{37}AB=

(6−5)

2

+(4−(−2))

2

=

1

2

+6

2

=

1+36

=

37

AC =\sqrt{(7-5)^2 + (-2 -(-2))^2} = \sqrt{2^2 + 0^2} = \sqrt{4 + 0} = \sqrt{4} = 2AC=

(7−5)

2

+(−2−(−2))

2

=

2

2

+0

2

=

4+0

=

4

=2

BC =\sqrt{(7-6)^2 + (-2 -4)^2} = \sqrt{1^2 + (-6)^2} = \sqrt{1 + 36} = \sqrt{37}BC=

(7−6)

2

+(−2−4)

2

=

1

2

+(−6)

2

=

1+36

=

37

AB = BC = √37

Hence verified that these vertices are of an isosceles triangles