Question 33 of 70intermediate🔧 ApplyShort Answer3 marks

Find the distance of the point (−1,1)(-1, 1) from the line 12(x+6)=5(y−2)12(x + 6) = 5(y - 2).

Correct Answer

5 units

Exercise: EXERCISE 9.3 | Q: 3 | (Page 17)
For More Understanding

Explanation

This question requires applying the distance formula from a point to a line, as demonstrated in Example 9 of the textbook. The student must first convert the given line equation to standard form Ax + By + C = 0, identify the coefficients A, B, C, and then apply the formula d = |Ax₁ + By₁ + C|/A2+B2\sqrt{A² + B²}.

Solution Steps

  1. Step 1: Convert the line equation to standard form. Given line: 12(x + 6) = 5(y - 2) Expanding: 12x + 72 = 5y - 10 Rearranging: 12x - 5y + 82 = 0 Here, A = 12, B = -5, C = 82

  2. Step 2: Identify the given point. Point (x₁, y₁) = (-1, 1)

  3. Step 3: Apply the distance formula. d = |Ax₁ + By₁ + C|/A2+B2\sqrt{A² + B²} d = |12(-1) + (-5)(1) + 82|/122+(−5\sqrt{12² + (-5}²) d = |-12 - 5 + 82|/144+25\sqrt{144 + 25} d = |65|/169\sqrt{169} d = 65/13 = 5 units

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