Question

A,B & C are the points (-8, -4), (-2, 6) and (4, -4) respectively. show that ABC is an isosceles triangle. find the perimeter of the triangle

Answer 1

xA = - 8 , yA = - 4

xB = - 2 , yB = 6

xC = 4 , yC = - 4


AB = √ ( ( xA - xB)² + ( yA - yB )² )

AB = √ ( ( - 8 - ( - 2) )² + ( - 4 - 6 )² )

AB = √ ( ( - 8 + 2)² + ( - 10 )² )

AB = √ ( ( - 6 )² + 100 )

AB = √ ( 36 + 100 )

AB = √ 136

AB = √ ( 4 ∙ 34 )

AB = √4 ∙ √34

AB = 2 √34


BC = √ ( ( xB - xC)² + ( yB - yC )² )

BC = √ ( ( - 2 - 4 )² + ( 6 - ( - 4 )² )

BC = √ ( ( - 6 )² + ( 6 + 4 )² )

BC = √ ( 36 + 10² )

BC = √ ( 36 + 100 )

BC= √ 136

BC = √ ( 4 ∙ 34 )

BC = √4 ∙ √34

BC = 2 √34


AC = √ ( ( xA - xC)² + ( yA - yC )² )

AC = √ ( ( - 8 - 4)² + ( - 4 - (- 4 ) )² )

AC = √ ( ( - 12 )² + ( - 4 + 4 )² )

AC = √ ( 144 + 0² )

AC = √ 144

AC = √12

Your triangle has two sides of equal length AB = 2 √34 and BC = 2 √34

So your triangle is isosceles triangle.

Perimeter:

P = AB + BC + AC

P = 2 √34 + 2 √34 + √12

P = 4 √34 + 12

P = 4 √34 + 4 ∙ 3

P = 4 ( √34 + 3 )