Question

represent the following equations on the graph determine the vertices of triangle so formed y=x,y=0 , 3x+3y = 10

Answer 1

Geometry problem

Given: Equations of the three sides of a triangle.

To find: The graph and the vertices of the triangle.

Solution:

Solution 1. Drawing the graph

The three equations are

y = x ..... (1)

y = 0 .....(2)

3x + 3y = 10 .....(3)

Clearly, the first equation makes an angle 45° with the positive x-axis and the equation y = 0 is the x-axis itself. The third equation 3x + 3y = 10 can be written as x/(10/3) + y/(10/3) = 1, and this it intersects the axes at (10/3, 0) and (0, 10/3).

Use the above conditions and you will find the required graph. [ See the given attachment. ]

Solution 2. Finding the vertices

We represent the equations as the three sides of the triangle OAB -

OA: y = x .....(1)

OB: y = 0 .....(2)

AB: 3x + 3y = 10 .....(3)

Solving (1) and (2), we get-

x = 0 and y = 0

i.e., the coordinates of O are (0, 0).

Solving (1) and (3), we get-

x = 5/3 and y = 5/3

i.e., the coordinates of A are (5/3, 5/3).

Solving (2) and (3), we get-

x = 10/3 and y = 0

i.e., the coordinates of B are (10/3, 0).

So the vertices of the given triangle are (0, 0), (5/3, 5/3) and (10/3, 0).