NIMCET 2022 — Mathematics PYQ

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Question

NIMCET 2022 — Mathematics PYQ

NIMCET | Mathematics | 2022

Area of the parallelogram formed by the lines y= 4x, y =4x + 1, x +y = 0 and x + y = 1 is

Choose the correct answer:

Explanation

Area Calculation

The area of a parallelogram formed by the lines

y = m x

,

y = m x + c_{1}

,

y = n x

, and

y = n x + c_{2}

can be calculated

using the formula:

Area = \frac{∣ c _{1} c _{2} ∣}{∣ m - n ∣}

.

Step-by-step Solution

1. The given equations of the lines are identified:

•

y = 4 x

•

y = 4 x + 1

•

x + y = 0 ⟹ y = - x

•

x + y = 1 ⟹ y = - x + 1

2. The parameters

m

,

n

,

c_{1}

, and

c_{2}

are extracted from the given equations:

• From

y = 4 x

and

y = 4 x + 1

, it is determined that

m = 4

and

c_{1} = 1

.

• From

y = - x

and

y = - x + 1

, it is determined that

n = - 1

and

c_{2} = 1

.

3. The values are substituted into the area formula:

Area = \frac{∣ ( 1 ) ( 1 ) ∣}{∣4 - ( - 1 ) ∣}

1. The calculation is performed:

Area = \frac{∣1∣}{∣4 + 1∣} = \frac{1}{5}

Final Answer

The area of the parallelogram is

\frac{1}{5}

.