If the three points A(1, 6), B(3, -4), and C( | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For three points $A(x_1, y_1)$, $B(x_2, y_2)$, and $C(x_3, y_3)$ to be collinear, the area of the triangle formed by them must be zero, or the slo

Vedclass · Accepted Answer

$5x + y - 11 = 0$

Vedclass · Answer

(A) For three points $A(x_1, y_1)$, $B(x_2, y_2)$, and $C(x_3, y_3)$ to be collinear, the area of the triangle formed by them must be zero, or the slope of $AB$ must equal the slope of $BC$. Using the determinant method: $\begin{vmatrix} 1 & 6 & 1 \ 3 & -4 & 1 \ x & y & 1 \end{vmatrix} = 0$ Expanding along the first row: $1(-4 - y) - 6(3 - x) + 1(3y - (-4x)) = 0$ $-4 - y - 18 + 6x + 3y + 4x = 0$ $10x + 2y - 22 = 0$ Dividing by $2$: $5x + y - 11 = 0$

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

Similar Questions

If the lines $x + 2ay + a = 0, x + 3by + b = 0$ and $x + 4cy + c = 0$ are concurrent,then $a, b$ and $c$ are in :-

The lines $15x - 18y + 1 = 0$,$12x + 10y - 3 = 0$ and $6x + 66y - 11 = 0$ are

For $c \neq 0, c \neq 1$,if the straight lines $x+y=1$,$2x-y=c$,and $bx+2by=c$ have one common point,then:

If the lines $4x + 3y = 1$,$y = x + 5$,and $5y + bx = 3$ are concurrent,then the value of $b$ is:

If the lines $x + q = 0$,$y - 2 = 0$,and $3x + 2y + 5 = 0$ are concurrent,then the value of $q$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module