Question

If the algebraic sum of distances of points (2,1), (3,2) and (–4, 7) from the line y = mx + c is zero, then this line will always pass through a fixed point whose co-ordinate is–

• A. (1, 3)
• B. (1, 10)
• C. (1, 6)
• D. $\left( \frac { 1 } { 3 } , \frac { 10 } { 3 } \right)$

Answer 1

Answer: (D)

$\left( \frac { 1 } { 3 } , \frac { 10 } { 3 } \right)$

Answer 2

P₁ + P₂ + P₃ = 0

+ + = 0

2m + 3m – 4m – 1 – 2 – 7 + 3c = 0

m – 10 + 3c = 0 mx – y + c = 0

$\frac { - 10 } { - y }$ = $\frac { 3 } { 1 }$ x = 1/3, y = 10/3