Question 20 of 70intermediate🔧 ApplyShort Answer3 marks

Find the equation of the line passing through (−3,5)(-3, 5) and perpendicular to the line through the points (2,5)(2, 5) and (−3,6)(-3, 6).

Correct Answer

5x - y + 20 = 0

Exercise: EXERCISE 9.2 | Q: 9 | (Page 14)
For More Understanding

Explanation

This question tests the concept of finding the equation of a line perpendicular to a given line. From the context, we use the two-point form to find the slope of the given line, then apply the perpendicularity condition (product of slopes = -1), and finally use the point-slope form to derive the required equation.

Solution Steps

  1. Step 1: Find slope of line through (2, 5) and (-3, 6) using formula m = (y₂ - y₁)/(x₂ - x₁) = (6 - 5)/(-3 - 2) = 1/(-5) = -1/5

  2. Step 2: Find slope of perpendicular line using condition m₁ × m₂ = -1. So m₂ × (-1/5) = -1, giving m₂ = 5

  3. Step 3: Apply point-slope form y - y₀ = m(x - x₀) for point (-3, 5) and slope 5: y - 5 = 5(x + 3)

  4. Step 4: Simplify: y - 5 = 5x + 15, therefore y = 5x + 20, or 5x - y + 20 = 0

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