Correct Answer - Option 2 : 2 units
Concept:
Perpendicular Distance of a Point from a Line:
Let us consider a line Ax + By + C = 0 and a point whose coordinate is (x1, y1)
\(\rm d=|\frac{Ax_1+By_1+C}{\sqrt{A^2+B^2}}|\)
Calculation:
Given: equation of line is 3x + 4y = 7 and a point is (3, 2)
We know the distance of a line from is given by, \(\rm d=|\frac{Ax_1+By_1+C}{\sqrt{A^2+B^2}}|\)
So, distance of a point (3, 2) from a line 3x + 4y - 7 = 0 is given by,
\(\rm d = |\frac{3(3)+4(2)-7}{\sqrt{3^2+4^2}}|\)
\(\rm = |\frac{9+8-7}{\sqrt{9+16}}|\)
\(\rm = |\frac{10}{\sqrt{25}}|\)
= 10/5
= 2 units
Hence, option (2) is correct.