Find the area of the quadrilateral formed by | vedclass

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

Question

(B) The given lines are of the form $ax + by + c_1 = 0$ and $ax + by + c_2 = 0$ (parallel pairs).Pair $1$: $3x - 4y + 1 = 0$ and $3x - 4y + 3 = 0$.Pai

Vedclass · Accepted Answer

$2/7$

Vedclass · Answer

(B) The given lines are of the form $ax + by + c_1 = 0$ and $ax + by + c_2 = 0$ (parallel pairs).Pair $1$: $3x - 4y + 1 = 0$ and $3x - 4y + 3 = 0$.Pair $2$: $4x - 3y - 1 = 0$ and $4x - 3y - 2 = 0$.The area of a parallelogram formed by lines $a_1x + b_1y + c_1 = 0, a_1x + b_1y + c_2 = 0, a_2x + b_2y + d_1 = 0,$ and $a_2x + b_2y + d_2 = 0$ is given by $\frac{|(c_1 - c_2)(d_1 - d_2)|}{|a_1b_2 - a_2b_1|}$.Here,$a_1 = 3, b_1 = -4, c_1 = 1, c_2 = 3$ and $a_2 = 4, b_2 = -3, d_1 = -1, d_2 = -2$.Area $= \frac{|(1 - 3)(-1 - (-2))|}{|(3)(-3) - (4)(-4)|} = \frac{|(-2)(1)|}{|-9 + 16|} = \frac{2}{7}$.

Find the area of the quadrilateral formed by the lines $4y - 3x = 1, 4y - 3x - 3 = 0, 3y - 4x + 1 = 0,$ and $3y - 4x + 2 = 0$.

Similar Questions

The four points whose coordinates are $(2, 1), (1, 4), (4, 5), (5, 2)$ form:

$A$ quadrilateral has distinct integer side lengths. If the second-largest side has length $10$,then the maximum possible length of the largest side is

Suppose a triangle is formed by $x+y=10$ and the coordinate axes. Then the number of points $(x, y)$ where $x$ and $y$ are natural numbers,lying inside the triangle is

Let $P$ be an interior point of a convex quadrilateral $ABCD$ and $K, L, M, N$ be the mid-points of $AB, BC, CD, DA$ respectively. If $\text{Area}(PKAN) = 25$,$\text{Area}(PLBK) = 36$,and $\text{Area}(PMDN) = 41$,then $\text{Area}(PLCM)$ is

If the vertices of a triangle are $(0, 2)$,$(1, 0)$,and $(3, 1)$,then the triangle is

Vedclass Test Series

Exam Paper Generator

Online Exam Module