The distance of the point (1, 2) from the lin | vedclass

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

Question

(C) Let the equation of the line parallel to $3x - y = 7$ be $3x - y = \lambda$. Since it passes through $(1, 2)$,this point must satisfy the equation

Vedclass · Accepted Answer

$\sqrt{40}$

Vedclass · Answer

(C) Let the equation of the line parallel to $3x - y = 7$ be $3x - y = \lambda$. Since it passes through $(1, 2)$,this point must satisfy the equation $3x - y = \lambda$. $	herefore 3(1) - 2 = \lambda \Rightarrow \lambda = 1$. So,the line is $3x - y = 1$. Now,we find the intersection of $x + y + 5 = 0$ and $3x - y = 1$. Adding the two equations: $(x + y + 5) + (3x - y) = 0 + 1$ $\Rightarrow 4x + 5 = 1$ $\Rightarrow 4x = -4$ $\Rightarrow x = -1$. Substituting $x = -1$ into $x + y + 5 = 0$: $-1 + y + 5 = 0 \Rightarrow y = -4$. So,the point of intersection is $(-1, -4)$. The required distance is the distance between $(1, 2)$ and $(-1, -4)$. Using the distance formula: $d = \sqrt{(1 - (-1))^2 + (2 - (-4))^2} = \sqrt{2^2 + 6^2} = \sqrt{4 + 36} = \sqrt{40}$.

The distance of the point $(1, 2)$ from the line $x + y + 5 = 0$ measured along the line parallel to $3x - y = 7$ is equal to

Similar Questions

The distance between the lines $3x - 2y = 1$ and $6x - 4y + 9 = 0$ is

If the length of the perpendicular from the origin to the line $x/a + y/b = 1$ is $p$,then which of the following is true for $a^2, 4p^2, b^2$?

Reduce the equation $x-y=4$ into the normal form $x \cos \omega + y \sin \omega = p$. Find the perpendicular distance from the origin $(p)$ and the angle between the perpendicular and the positive $x$-axis $(\omega)$.

If $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line $x+y+3=0$ such that each of them is at a distance of $\sqrt{5}$ units from the line $x+2y+2=0$,then the value of $|x_1-x_2|$ is:

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module