Math, asked by divyeshkher19, 8 months ago

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

Answered by RvChaudharY50
1

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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