Question

The area of the parallelogram formed by the lines 4y-3x=1,4y-3x-3=0,3y-4x+1,3y-4x+2=0 is

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

Equation 1:

⇒3x−4y+1=0⇒4y=3x+1⇒y=34x+14

Hence, m1=34 and c1=14

Equation 2:

⇒3x−4y+3=0⇒4y=3x+3⇒y=34x+34

Hence, c2=34

Equation 3:

⇒4x−3y−1=0⇒3y=4x−1⇒y=43x−13

Hence, m2=43 and d1=−13

Equation 4:

⇒4x−3y−2=0⇒3y=4x−2⇒y=43x−23

Hence, d2=−23

Now, area of parallelogram is given by

⇒ Area of parallelogram=∣∣∣(c1−c2)(d1−d2)m1−m2∣∣∣

Therefore,

⇒Area of parallelogram=∣∣∣∣∣∣(14−34)(−13−(−23))34−43∣∣∣∣∣∣

=∣∣∣∣∣∣(−24)(−13+23)9−1612∣∣∣∣∣∣=∣∣∣∣∣∣(−12)(13)−712∣∣∣∣∣∣=∣∣∣∣∣16712∣∣∣∣∣=∣∣∣1×126×7∣∣∣=∣∣∣27∣∣∣=27

Step-by-step explanation: