Q. 185.0( 1 Vote )

The points A(0, 3), B(-2, a) and C(-1, 4) are the vertices of a Î ABC right âangledat A. Find the value of a.

Answer :

SOLUTION:

Given, the vertices of a Δ ABC are right –angled at A.

Using Pythagoras theorem

⇒ AB ^{ 2 } + AC ^{ 2 } = BC ^{ 2 }

AB ^{ 2 } = (- 2 - 0) ^{ 2 } + (a - 3) ^{ 2 } = 4 + (a – 3) ^{ 2 }

BC ^{ 2 } = (- 1 + 2) ^{ 2 } + (4 - a) ^{ 2 } = 1 + (4 – a) ^{ 2 }

AC ^{ 2 } = (- 1 - 0) ^{ 2 } + (4 - 3) ^{ 2 } = 1 + 1 = 2

Since, AB ^{ 2 } + AC ^{ 2 } = BC ^{ 2 }

⇒ 4 + (a – 3) ^{ 2 } + 2 = 1 + (4 – a) ^{ 2 }

⇒ 4 + a ^{ 2 } + 9 – 6a + 2 = 1 + 16 + a ^{ 2 } – 8a

⇒ 2a = 2

∴ a = 1.

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