Question

Consider four straight lines
(i) l₁; 3y = 4x + 5
(ii) l₂; 4y = 3x – 1
(iii) l₃; 4y + 3x = 7
(iv) l₄; 4x + 3y = 2
Which of the following statement is true?

Options

• l₁ and l₂ are perpendicular

• l₂ and l₄ are parallel

• l₂ and l₄ are perpendicular

• l₂ and l₃ are parallel

Answer 1

l₂ and l₄ are perpendicular

Explanation;

Hint:

Slope of l₁ = `4/3`;

Slope of l₂ = `3/4`;

Slope of l₃ = `-3/4`;

Slope of l₄ = `-4/3`

(i) l₁ × l₂ = `4/3 xx 3/4` = 1   ...(False)

(ii) l₁ = `4/3`; l₄ = `-4/3` not parallel  ...(False)

(iii) l₂ × l₄ = `3/4 xx - 4/3` = − 1   ...(True)

(iv) l₂ = `3/4`; l₃ = `-3/4` not parallel   ...(False)