Question

Which one of the the following is the nearest point on the line 3x- 4y = 25 from the origin?

• A. (-1, -7)
• B. (3, -4)
• C. ( -5, -8)
• D. (3, 4)

Answer 1

Answer: (B)

Only two point A (-1, - 7) and B (3, 4) satisfy the given equation of the line 3x - 4y = 25 Distance of A (- 1, - 7) from the origin O.
$=\sqrt{{\left(0+1\right)}^2+{\left(0+7\right)}^2}=\sqrt{50}=5\sqrt{2}$
Distance of B (3, - 4) from the origin O.
$=\sqrt{{\left(0-3\right)}^2+{\left(0+4\right)}^2}=\sqrt{9+16}=\sqrt{25}=5$
The nearest point is (3, - 4)