Question

find the area of triangle formed by the lines x=3,y=4andx=y​

Answer 1

Step-by-step explanation:

x = 3 y = 4 x = y eq:1 ) a line parallel to y axis

.

eq 2: 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 = 1 2 12 x | x1 x (y2 – y3) + x2 x (y3 – y1) + x3 x (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 =  1 2 12 x| 3 x (4– 3) + 4 x (3 – 4) + 3 x (4– 4) | Area = 1 2 12 x | 3 x (1) + 4 x ( – 1) + 3 x (0) | Area = 1 2 12 x | 3– 4 | ⇒ Area =  1 2 12 sq. units

The Area of the triangle is  1 2 12 sq. units