What is the equation of the altitude through B on A C ? [NDA-II 2021]

Correct Answer is : 2x−y−5=02x-y-5=02x−y−5=0

Correct Answer is : 2x−y−5=02x-y-5=02x−y−5=0

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UPSC NDA 2 2021 Mathematics Solved Paper

Direction : Consider the following for the next two (02) items that follow.

The equations of the sides

A B, B C

and

C A

of a triangle

A B C

are

x-2=0, y+1=0

and

x+2 y-4=0

respectively.

[NDA-II 2021]

Question : 57 of 120

Marks: +1, -0

B

A C

Solution: 👈: Video Solution

(d) Equation of

A B \Rightarrow x-2=0

Equation of

B C \Rightarrow y+1=0

Equation of

A C \Rightarrow x+2y-4=0

On solving Eq. (i) and Eq. (ii), we get

x = 2, y = -1

B = (2, -1)

\text{Slope of } A C = \frac{-\text{coefficient of } x}{\text{coefficient of } y}

m_{1} = -\frac{1}{2}

\therefore

Slope of altitude

B D = \frac{-1}{m_{1}} = \frac{-1}{-\frac{1}{2}} = 2

\therefore

Equation of altitude

B D

drawn from

B

A C

having slope 2 .

y+1 = 2(x-2)

y+1 = 2x-4

\Rightarrow 2x-y-5 = 0

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