Q. 175.0( 2 Votes )

The area of the triangle formed by the lines 2x + 3y = 12, x – y – 1 = 0 and x = 0 (as shown in Fig. 3.23) , is


A. 7 sq. units

B. 7.5 sq. units

C. 6.5 sq. units

D. 6 sq. units

Answer :

Given

Equation 1: 2x + 3y = 12 Equation 2: x – y = 1 Equation 3: x = 0


To calculate the Area at first we solve the Equation 1 & 2 Simultaneously by method of substitution.


We substitute the value of x from Equation 2 in Equation 1 to get the value of y


Equation 2: x – y = 1 x = y + 1


Equation 1: 2x + 3y = 12


Substituting the value from equation 2 we get


2(y + 1) + 3y = 12 2y + 2 + 3y = 12 5y = 10 y = 2


Putting the value in Equation 1 we get


x = 2 + 1 x = 3


So both this lines passes through ( 3 , 2) Let this Coordinate name be P1


Equation 3 is the equation for y axis


Equation 1 meets Y axis at (0 ,4) which is calculated by substituting x = 0 in Equation 1. Let this Coordinate name be P2


Equation 2 meets Y axis at (0 , – 1) which is calculated by substituting x = 0 in Equation 2. Let this Coordinate name be P3


So Area of the triangle = *| x1 * (y2 – y3) + x2 * (y3 – y1) + x3 * (y1 – y2) |


Where x1 ,y1 are the coordinates of P1


x2, y2 are the coordinates of P2


x3 ,y3 are the coordinates of P3


Area of the Given Triangle = *| 3* (4+ 1) + 0 * ( – 1 – 2) + 0* (2– 4) |


Area of the Given Triangle = *| 3* 5 |


Area = Area = 7.5 Sq. Units


Area of the triangle is 7.5 sq. Units

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