Find the equation of the line joining (1, 2) | vedclass

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

Question

(A) Let $P(x, y)$ be any point on the line joining the points $A(1, 2)$ and $B(3, 6)$. Since the points $A, B,$ and $P$ are collinear,the area of the

Vedclass · Accepted Answer

$y = 2x$

Vedclass · Answer

(A) Let $P(x, y)$ be any point on the line joining the points $A(1, 2)$ and $B(3, 6)$. Since the points $A, B,$ and $P$ are collinear,the area of the triangle formed by these three points must be zero.The area of a triangle with vertices $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ is given by $\frac{1}{2} |\det(M)| = 0$,where $M = \begin{bmatrix} x_1 & y_1 & 1 \ x_2 & y_2 & 1 \ x_3 & y_3 & 1 \end{bmatrix}$.Substituting the given points:$\frac{1}{2} \left| \begin{matrix} 1 & 2 & 1 \ 3 & 6 & 1 \ x & y & 1 \end{matrix} ight| = 0$Expanding the determinant along the first row:$1(6(1) - y(1)) - 2(3(1) - x(1)) + 1(3y - 6x) = 0$$(6 - y) - 2(3 - x) + (3y - 6x) = 0$$6 - y - 6 + 2x + 3y - 6x = 0$Combining like terms:$(2x - 6x) + (3y - y) + (6 - 6) = 0$$-4x + 2y = 0$$2y = 4x$$y = 2x$Thus,the equation of the line is $y = 2x$.

Find the equation of the line joining $(1, 2)$ and $(3, 6)$ using determinants.

Similar Questions

The value of the determinant $\left| \begin{array}{ccc} 0 & b^3 - a^3 & c^3 - a^3 \\ a^3 - b^3 & 0 & c^3 - b^3 \\ a^3 - c^3 & b^3 - c^3 & 0 \end{array} \right|$ is equal to:

The area of a triangle with vertices $(-3, 0)$,$(3, 0)$,and $(0, k)$ is $9$ sq units. Find the value of $k$.

If $w = \frac{-1-i \sqrt{3}}{2}$ where $i = \sqrt{-1}$,then the value of $\left|\begin{array}{ccc}1 & w & w^2 \\ w & w^2 & 1 \\ w^2 & 1 & w\end{array}\right|$ is

Evaluate the determinant: $\left| \begin{array}{lll} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \end{array} \right|$

If $\left|\begin{array}{lll}1 & 2 & 3 \\ 2 & 3 & 4 \\ 3 & 4 & 5\end{array}\right|=2016 k$,then $k=$ . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module