Let the lines be L_1: 2x + 3y - 7 = 0 and L_2 | vedclass

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

Question

(D) The given lines are $L_1: 2x + 3y - 7 = 0$ and $L_2: 2x + 3y - 12 = 0$.For point $A(3, -5)$,evaluate the expressions:$L_1(3, -5) = 2(3) + 3(-5) -

Vedclass · Accepted Answer

None of these.

Vedclass · Answer

(D) The given lines are $L_1: 2x + 3y - 7 = 0$ and $L_2: 2x + 3y - 12 = 0$.For point $A(3, -5)$,evaluate the expressions:$L_1(3, -5) = 2(3) + 3(-5) - 7 = 6 - 15 - 7 = -16 $L_2(3, -5) = 2(3) + 3(-5) - 12 = 6 - 15 - 12 = -21 Since both values have the same sign,point $A$ does not lie between the lines.Perpendicular distance $d_1$ from $A$ to $L_1$ is $\frac{|2(3) + 3(-5) - 7|}{\sqrt{2^2 + 3^2}} = \frac{|-16|}{\sqrt{13}} = \frac{16}{\sqrt{13}}$.Perpendicular distance $d_2$ from $A$ to $L_2$ is $\frac{|2(3) + 3(-5) - 12|}{\sqrt{2^2 + 3^2}} = \frac{|-21|}{\sqrt{13}} = \frac{21}{\sqrt{13}}$.The distance between the parallel lines is $d = \frac{|c_1 - c_2|}{\sqrt{a^2 + b^2}} = \frac{|-7 - (-12)|}{\sqrt{2^2 + 3^2}} = \frac{5}{\sqrt{13}}$.Thus,none of the given options $A, B, C$ are correct.

Let the lines be $L_1: 2x + 3y - 7 = 0$ and $L_2: 2x + 3y - 12 = 0$. For the point $A(3, -5)$,which of the following is true?

Similar Questions

$O(0,0), B(-3,-1), C(-1,-3)$ are vertices of a triangle $OBC$. $D$ is a point on $OC$ and $E$ is a point on $OB$. If the equation of $DE$ is $2x + 2y + \sqrt{2} = 0$,then the ratio in which the line $DE$ divides the altitude of the triangle $OBC$ from $O$ to $BC$ is:

The ratio in which the line $3x + 4y + 2 = 0$ divides the distance between $3x + 4y + 5 = 0$ and $3x + 4y - 5 = 0$ is:

Choose the correct statement which describes the position of the point $(-6, 2)$ relative to the straight lines $2x + 3y - 4 = 0$ and $6x + 9y + 8 = 0$.

What is the length of the perpendicular from the point $(3, 4)$ to the line $3x + 4y + 10 = 0$?

The distance of the line $2x - 3y = 4$ from the point $(1, 1)$ measured parallel to the line $x + y = 1$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module