Q. 245.0( 2 Votes )

# The equation of t A. x – y = 5

B. x + y = 5

C. x + y = 1

D. x – y = 1

Answer :

Given that straight line passing through the point (3, 2)

and perpendicular to the line y = x

Let the equation of line ‘L’ is

y – y_{1} = m(x – x_{1})

Since, L is passing through the point (3, 2)

∴ y – 2 = m(x – 3) …(i)

Now, given eq. is y = x

Since, the above equation is in **y = mx + b** form

So, the slope of this equation is 1

It is also given that line L and y = x are perpendicular to each other.

We know that, when two lines are perpendicular, then

m_{1} × m_{2} = -1

∴ m × 1 = -1

⇒ m = -1

Putting the value of m in eq. (i), we get

y – 2 = (-1)(x – 3)

⇒ y – 2 = -x + 3

⇒ x + y = 3 + 2

⇒ x + y = 5

Hence, the correct option is **(b)**

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