Q. 165.0( 1 Vote )

The area of the t A. 1/2 sq. unit

B. 1 sq. unit

C. 2 sq. unit

D. None of these

Answer :

Given :


Equation 1: x = 3


Equation 2: y = 4


Equation 3: x = y



Equation 1 is a line parallel to y axis


Equation 2 is a line parallel to x axis


So Equation 1 & 2 are mutually perpendicular to each other.


Hence the triangle formed is a right angled triangle.


First we solve the three lines simultaneously by method of substitution and get the three points of intersection or three coordinates of the triangle.


Solving Equation 1 & 2 we get the coordinate ( 3, 4 ). Let this Coordinate name be P1


Solving Equation 2 & 3 we get the coordinate ( 4 ,4 ). Let this Coordinate name be P2


Solving Equation 3 & 1 we get the coordinate ( 3 ,3 ). Let this Coordinate name be P3


We now use the formula for Area of a triangle through 3 given points


Area = *| 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– 3) + 4 * (3 – 4) + 3* (4– 4) |


Area = *| 3* (1) + 4 * ( – 1) + 3* (0) |


Area = *| 3– 4 | Area = sq. units


The Area of the triangle is sq. units

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