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UI Post-UTME Mathematics 2025 (Model questions) Question 6

Question 6

Coordinate Geometry

A line passes through the point (2, −1) and is perpendicular to the line 3x − 2y + 7 = 0. Find its equation

  1. A.2x + 3y − 1 = 0
  2. B.2x + 3y − 7 = 0
  3. C.3x + 2y − 4 = 0
  4. D.2x + 3y − 1 = 3
Show the answer and explanation

Answer: A (2x + 3y − 1 = 0)

Explanation

The given line has gradient 3/2, so the perpendicular has gradient −2/3. y + 1 = −2/3(x − 2) gives 3y + 3 = −2x + 4, i.e. 2x + 3y − 1 = 0.