The lines 2x + 3y = 6 and 2x + 3y = 8 cut the | vedclass

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

Question

(A) The given lines are $2x + 3y = 6$ and $2x + 3y = 8$.To find the $X$-intercepts,set $y = 0$:For $2x + 3y = 6$,$2x = 6 \Rightarrow x = 3$. So,$A = (

Vedclass · Accepted Answer

$2x + 3y = 10$

Vedclass · Answer

(A) The given lines are $2x + 3y = 6$ and $2x + 3y = 8$.To find the $X$-intercepts,set $y = 0$:For $2x + 3y = 6$,$2x = 6 \Rightarrow x = 3$. So,$A = (3, 0)$.For $2x + 3y = 8$,$2x = 8 \Rightarrow x = 4$. So,$B = (4, 0)$.The line $L$ passes through $(2, 2)$ and cuts the $X$-axis at $C(x_1, 0)$.Given that the abscissae of $A, B,$ and $C$ are in arithmetic progression,we have $3, 4, x_1$ in $AP$.Thus,$2(4) = 3 + x_1$ $\Rightarrow 8 = 3 + x_1$ $\Rightarrow x_1 = 5$.So,the point $C$ is $(5, 0)$.The equation of the line $L$ passing through $(2, 2)$ and $(5, 0)$ is given by:$y - 0 = \frac{2 - 0}{2 - 5}(x - 5)$$y = \frac{2}{-3}(x - 5)$$-3y = 2x - 10$$2x + 3y = 10$

The lines $2x + 3y = 6$ and $2x + 3y = 8$ cut the $X$-axis at $A$ and $B$,respectively. $A$ line $L$ drawn through the point $(2, 2)$ meets the $X$-axis at $C$ in such a way that the abscissae of $A, B,$ and $C$ are in arithmetic progression. Then,the equation of the line $L$ is

Similar Questions

The equation of the line passing through $(1, 2)$ and perpendicular to $3x + 4y + 5 = 0$ is

If the points $A(5, k)$,$B(-3, 1)$ and $C(-7, -2)$ are collinear,then $k=$

The opposite vertices of a square are $(1, 2)$ and $(3, 8)$. Then,the equation of the diagonal of the square passing through the point $(1, 2)$ is:

Find the equations of the sides $QR$ and $RP$ of a triangle $PQR$ where $P = (2, 1)$,and the sides $QR$ and $RP$ have slopes $m_1 = \frac{2}{\sqrt{3}}$ and $m_2 = -\frac{2}{\sqrt{3}}$ respectively,passing through the origin $(0, 0)$ for $QR$ and intersecting at $P(2, 1)$ for $RP$.

The equation of the straight line making equal intercepts on the axes and passing through the point $(2, 4)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module