proov that the point (0,0),(5,5)and (-5,5)are vertices of a right isosceles
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Let the Points be represented as :
A(0,0), B(5,5), C(-5,5)
Then, clearly, by Distance formula...
AB = √[ ( 5-0 )² + ( 5 - 0 )² ] = 5√2
BC = √[ (5-5)² + (5+5)² ] = 10
Similarly, AC = 5√2
Now, AB = AC ..
Also.
AB² + AC² = 50 + 50 = 100 = BC²
.'. By converse of pythagoras, ABC is an isosceles right Δ
A(0,0), B(5,5), C(-5,5)
Then, clearly, by Distance formula...
AB = √[ ( 5-0 )² + ( 5 - 0 )² ] = 5√2
BC = √[ (5-5)² + (5+5)² ] = 10
Similarly, AC = 5√2
Now, AB = AC ..
Also.
AB² + AC² = 50 + 50 = 100 = BC²
.'. By converse of pythagoras, ABC is an isosceles right Δ
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