show that the points (1,1),(4,4) and (6,2) are vertices of a right angled triangle chapter 7 ncert class 10 plz no fake anwers
Answers
Question :- show that the points (1,1),(4,4) and (6,2) are vertices of a right angled triangle ?
Solution :-
Let us assume that, A(1,1) , B(4,4) and C(6,2) are the vertices of a right angled ∆ .
Than,
→ AB = √[(x2 - x1)² + (y2 - y1)²]
→ AB = √[(4 - 1)² + (4 - 1)²]
→ AB = √[3² + 3²]
→ AB = √(9 + 9)
→ AB = √(18)
→ AB = 3√2 units.
Similarly,
→ BC = √[(x2 - x1)² + (y2 - y1)²]
→ BC = √[(6 - 4)² + (2 - 4)²]
→ BC = √[2² + (-2)²]
→ BC = √(4 + 4)
→ BC = √(8)
→ BC = 2√2 units.
and,
→ AC = √[(x2 - x1)² + (y2 - y1)²]
→ AC = √[(6 - 1)² + (2 - 1)²]
→ AC = √[5² + 1²]
→ AC = √(25 + 1)
→ AC = √(26)
→ AC = √26 units.
Now, here AC is the longest side. if ABC is a right angle, then pythagoras theorem will satisfy ,
→ AB² + BC² = AC²
→ (3√2)² + (2√2)² = (√26)²
→ 18 + 8 = 26
→ 26 = 26 .
Therefore, Here pythagoras theorem satisfy. Then, ∆ABC is a right angle triangle where AC is the hypotenuse.
Hence, given points are vertices of a right angled triangle.
Learn more :-
Prove that the points A(0, -1), B(-2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?
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