Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too!

The equation of the straight line passing

Question:

The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is
A. x – y = 5
B. x + y = 5
C. x + y = 1
D. x – y = 1

Solution:

B. x + y = 5

Explanation:

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 – y1 = m(x – x1)

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

m1 × m2 = -1

∴ m × 1 = -1

⇒ m = -1

Putting the value of m in equation (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)

Leave a comment

None
Free Study Material