Question

1. The straight lines kx + 2y = 1 and 4x - y = 3 are perpendicular then `k = 1/2`.
2. Two points form a line are y − y₁ = m(x − x₁).

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (i)

Explanation:

⇒ Going through (i) statement,

For two lines to be perpendicular, the product of their slopes must be −1,

Slope of first line (m₁): `-k/2`

Slope of second line (m₂): `-4/(-1)` = 4

Let’s calculate:

`(- k/2) xx 4 = -1`

−2k = −1

∴ k = 1/2

This matches the statement, so the statement is valid.

⇒ Going through (ii) statement,

The formula y − y₁ = m(x − x₁) is specifically called the Point-Slope Form.

The Two-Point Form of a line is written by replacing m with the slope formula:

`y - y_1 = (y_2 - y_1)/(x_2 - x_1) (x - x_1)`

So, this statement is invalid.