A rectangle is formed by the lines x=0, x=3, | vedclass

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

Question

(D) The rectangle is bounded by $x=0, x=3, y=0, y=4$. The center of the rectangle is $(\frac{3}{2}, 2)$.Any line that divides the rectangle into two e

Vedclass · Accepted Answer

$2\sqrt{10}$

Vedclass · Answer

(D) The rectangle is bounded by $x=0, x=3, y=0, y=4$. The center of the rectangle is $(\frac{3}{2}, 2)$.Any line that divides the rectangle into two equal areas must pass through its center $(\frac{3}{2}, 2)$.The line $L$ is perpendicular to $3x+y+6=0$. The slope of $3x+y+6=0$ is $-3$, so the slope of line $L$ is $\frac{1}{3}$.The equation of line $L$ passing through $(\frac{3}{2}, 2)$ with slope $\frac{1}{3}$ is:$y - 2 = \frac{1}{3}(x - \frac{3}{2})$$3y - 6 = x - \frac{3}{2}$$6y - 12 = 2x - 3$$2x - 6y + 9 = 0$.The distance of the point $(\frac{1}{2}, -5)$ from the line $2x - 6y + 9 = 0$ is:$d = \frac{|2(\frac{1}{2}) - 6(-5) + 9|}{\sqrt{2^2 + (-6)^2}}$$d = \frac{|1 + 30 + 9|}{\sqrt{4 + 36}}$$d = \frac{40}{\sqrt{40}} = \sqrt{40} = 2\sqrt{10}$.

$A$ rectangle is formed by the lines $x=0, x=3, y=0$ and $y=4$. Let the line $L$ be perpendicular to $3x+y+6=0$ and divide the area of the rectangle into two equal parts. Then the distance of the point $(\frac{1}{2}, -5)$ from the line $L$ is equal to:

Similar Questions

What are the points on the $y$-axis whose distance from the line $\frac{x}{3}+\frac{y}{4}=1$ is $4$ units?

If $p$ and $q$ are the lengths of the perpendiculars from the origin to the lines $x \cos \theta - y \sin \theta = k \cos 2 \theta$ and $x \sec \theta + y \csc \theta = k$ respectively,prove that $p^{2} + 4q^{2} = k^{2}$.

The perpendicular distance from the point $(1, \pi)$ to the line joining $(1, 0^{\circ})$ and $(1, \frac{\pi}{2})$ (in polar coordinates) is

Let $f(\theta)$ be the distance of the line $(\sqrt{\sin \theta})x + (\sqrt{\cos \theta})y + 1 = 0$ from the origin. Then the range of $f(\theta)$ is -

$A$ straight line passes through the points $(5,0)$ and $(0,3)$. The length of the perpendicular from the point $(4,4)$ to the line is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module