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What is the distance from the point (3, 4) to the line defined by the equation 2

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Question: What is the distance from the point (3, 4) to the line defined by the equation 2x + 3y - 12 = 0?

Options:

  1. 2
  2. 3
  3. 1
  4. 4

Correct Answer: 2

Solution: 

Using the formula for distance from a point to a line: d = |Ax + By + C| / √(A² + B²), where A=2, B=3, C=-12. d = |2*3 + 3*4 - 12| / √(2² + 3²) = |6 + 12 - 12| / √13 = 6/√13.

What is the distance from the point (3, 4) to the line defined by the equation 2

Practice Questions

Q1
What is the distance from the point (3, 4) to the line defined by the equation 2x + 3y - 12 = 0?
  1. 2
  2. 3
  3. 1
  4. 4

Questions & Step-by-Step Solutions

What is the distance from the point (3, 4) to the line defined by the equation 2x + 3y - 12 = 0?
  • Step 1: Identify the point and the line. The point is (3, 4) and the line is given by the equation 2x + 3y - 12 = 0.
  • Step 2: Rewrite the line equation in the form Ax + By + C = 0. Here, A = 2, B = 3, and C = -12.
  • Step 3: Use the distance formula from a point (x0, y0) to a line Ax + By + C = 0, which is d = |Ax0 + By0 + C| / √(A² + B²).
  • Step 4: Substitute the values into the formula. Here, x0 = 3, y0 = 4, A = 2, B = 3, and C = -12.
  • Step 5: Calculate the numerator: |2*3 + 3*4 - 12| = |6 + 12 - 12| = |6| = 6.
  • Step 6: Calculate the denominator: √(A² + B²) = √(2² + 3²) = √(4 + 9) = √13.
  • Step 7: Divide the numerator by the denominator to find the distance: d = 6 / √13.
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