Find the distance between parallel lines

Question 35 of 70intermediate🔧 ApplyShort Answer4 marks

(i)

$15x + 8y - 34 = 0$ and $15x + 8y + 31 = 0$

Answer

The distance between the parallel lines is $\frac{65}{17}$ units.

(ii)

$l(x + y) + p = 0$ and $l(x + y) - r = 0$

Answer

The distance between the parallel lines is $\frac{|p + r|}{l\sqrt{2}}$ units.

Explanation

This question tests the application of the formula for distance between parallel lines. The context provides the formula: d = |C₁ - C₂|/ $\sqrt{A² + B²}$ for parallel lines in general form Ax + By + C = 0. For part (i), students identify A=15, B=8, C₁=-34, C₂=31 and apply the formula directly. For part (ii), students must first expand the equations to identify coefficients, then apply the same formula.

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