Question

the area of the triangle formed by the line x is equals to 3 Y is equals to 4 and X is equals to Y is ​

Answer 1

Answer:

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 = 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. unitsRead more on Sarthaks.com - https://www.sarthaks.com/1077115/the-area-of-the-triangle-formed-by-the-lines-y-and-is-sq-unit-b-sq-unit-c-2-sq-unit-d-none-of-these