The equation of the straight line passing through the point (3, 2) and

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

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

Answer»

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)