If the three points A(1,6), B(3, -4) and C(x, y) are collinear then the equation satisfying by x and y is

Question

If the three points A(1,6), B(3, -4) and C(x, y) are collinear then the equation satisfying by x and y is (A) 5x + y - 11= 0 (B) 5x + 13y + 5 = 0 (C) 5x -13y + 5 = 0 (D) 13x -5y +5 = 0

Tardigrade Admin · Accepted Answer

Since, the points A(1,6), B(3,-4) and C(x, y) are collinear. ∴ |1 6 1 3 -4 1 x y 1|=0 ⇒ 1(-4-y)-6(3-x)+1(3 y+4 x)=0 ⇒ 10 x+2 y-22=0 ⇒ 5 x+y-11=0

Q. If the three points $A (1, 6), B (3, - 4)$ and $C (x, y)$ are collinear then the equation satisfying by $x$ and $y$ is

$5 x + y - 11 = 0$

$5 x + 13 y + 5 = 0$

$5 x - 13 y + 5 = 0$

$13 x - 5 y + 5 = 0$

Since, the points $A (1, 6), B (3, - 4)$ and $C (x, y)$ are collinear.
$∴ ∣ ∣ 13 x 6 - 4 y 111 ∣ ∣ = 0$
$\Rightarrow 1 (- 4 - y) - 6 (3 - x) + 1 (3 y + 4 x) = 0$
$\Rightarrow 10 x + 2 y - 22 = 0$
$\Rightarrow 5 x + y - 11 = 0$

Q. If the three points A(1,6),B(3,−4) and C(x,y) are collinear then the equation satisfying by x and y is

5x+y−11=0

5x+13y+5=0

5x−13y+5=0

13x−5y+5=0