Question

5. Determine graphically the vertices of the triangle, the equations of whose sides are y = x, y = 0, x + y = 4

Ans: ( 0 , 0 ) , ( 4 , 0 ) , ( 2 , 2 )

Standard:- 10

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Answer 1

We are given three equations of straight lines, and these lines form the three sides of a triangle.

The intersection points of these lines are the vertices of the triangle. So we must first plot the graphs of these three lines.


$\rightarrow y=x$

Clearly, the value of x is same as y. So, we possible solutions for this line are (1,1), (2,2), (3,3) etc. Joining any two such points gives us the graph of $y=x$

$\rightarrow y=0$

We see that whatever value of x we take, the value of y is going to be zero. So possible solutions include (1,0), (2,0), (3,0) etc.

In fact, $y=0$ is the equation of the X-Axis.


$\rightarrow x+y=4$

We need points (x,y) which satisfy the above equation.


Suppose x=1, then we have y=3 from the above equation. So (1,3) is a solution of $x+y=4$

Similarly, if we take x=0, we have y=4. So (4,0) is also a solution. 

Joining (1,3) and (0,4) gives us the graph of this line.




Now we just have to see where these lines intersect. The point where two of the three lines intersect is a vertex. 

A graph is attached.

From the graph, it is clear that the intersection points are (0,0), (4,0), (2,2).

Thus, The vertices of the triangle are (0,0), (4,0) and (2,2).