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Problem 8 - Entrance Test

Find the distance of the point (1, 2) from the line 3x - 4y - 5 = 0.

Correct: A

The distance of a point (x1, y1) from the line Ax + By + C = 0 is |Ax1 + By1 + C|/√(A^2 + B^2). Here (x1, y1) = (1, 2) and the line is 3x - 4y - 5 = 0, so A = 3, B = -4, C = -5. So the distance is |3*1 - 4*2 - 5|/√(3^2 + (-4)^2) = |3 - 8 - 5|/√(9 + 16) = |-10|/√25 = 10/5 = 2.