Question

Prove that the points (3,0) ,(6,4) and (-1,3) are the vertices of a right angle issocles triangle

Answer 1

A(3,0)
B(6,4)
C(-1,3)
Find the distances of AB, BC and AC using the distance formula.
And then prove that hypotenuse² = Base² + Altitude²
Sry I can't solve this because I don't know how to type equation in this site...

Answer 2

Hi Julie,

Let A(3,0) , B(6,4),C(-1,3) vertices of a triangle
Now, By distance formula find the length of AB=√(6-3)²+(4-0)²
                                         
                                                                          =√3²+4²

                                                                          =√9+16

                                                                          =√25
                
                                                                          =5cm
And the length of AC=√(-1-3)²+(3-0)²

                                 =√(-4)²+3²

                                 =√16+9

                                 =√25

                                 =5cm
length of BC=√(-1-6)²+(3-4)²

                    =√49+1

                    =√50 cm

Now USING PGT H²=B²+P²
                       (√50)²=5²+5²
                       50   =25+25
AS H²=B²+P²
so these coordinates form a right angled triangle
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