If two sides of a square are 4x + 3y - 20 = 0 | vedclass

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

Question

(D) The given equations of the lines are $4x + 3y - 20 = 0$ and $4x + 3y + 15 = 0$. Since the coefficients of $x$ and $y$ are the same,the lines are p

Vedclass · Accepted Answer

$49$ sq. units

Vedclass · Answer

(D) The given equations of the lines are $4x + 3y - 20 = 0$ and $4x + 3y + 15 = 0$. Since the coefficients of $x$ and $y$ are the same,the lines are parallel. The distance $d$ between two parallel lines $ax + by + c_1 = 0$ and $ax + by + c_2 = 0$ is given by $d = \left| \frac{c_1 - c_2}{\sqrt{a^2 + b^2}} \right|$. Here,$a = 4$,$b = 3$,$c_1 = -20$,and $c_2 = 15$. $d = \left| \frac{-20 - 15}{\sqrt{4^2 + 3^2}} \right| = \left| \frac{-35}{\sqrt{16 + 9}} \right| = \left| \frac{-35}{5} \right| = 7$ units. Since the distance between two opposite sides of a square is equal to its side length $s$,we have $s = 7$ units. The area of the square is $s^2 = 7^2 = 49$ sq. units.

If two sides of a square are $4x + 3y - 20 = 0$ and $4x + 3y + 15 = 0$,then the area of the square is

Similar Questions

If $2p$ is the length of the perpendicular from the origin to the line $\frac{x}{a} + \frac{y}{b} = 1$,then:

Let two points be $A(1, -1)$ and $B(0, 2)$. If a point $P(x', y')$ is such that the area of $\Delta PAB = 5 \; \text{sq units}$ and it lies on the line $3x + y - 4\lambda = 0$,then a value of $\lambda$ is

The distance between the lines $3x + 4y = 9$ and $6x + 8y = 15$ is equal to units.

Let the origin be the centroid of an equilateral triangle $ABC$ and one of its sides be along the straight line $x+y=3$. If $R$ and $r$ are its circumradius and inradius respectively,then $R+r=$

The distance between the lines $4x + 3y = 11$ and $8x + 6y = 15$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module