Determine graphically the vertices of the triangle, the equations of whose sides are given below:
y=x, y=0 and 3x+3y=10
$ {\text{A}}{\text{. }}\left( {0,0} \right),\left( {\dfrac{{10}}{3},0} \right),\left( {\dfrac{5}{3},\dfrac{5}{3}} \right) \\
{\text{B}}{\text{. }}\left( {0,0} \right),\left( {\dfrac{{17}}{3},0} \right),\left( {\dfrac{5}{3},\dfrac{5}{3}} \right) \\
{\text{C}}{\text{. }}\left( {0,0} \right),\left( {\dfrac{{14}}{3},0} \right),\left( {\dfrac{5}{3},\dfrac{5}{3}} \right) \\
{\text{D}}{\text{. }}\left( {0,0} \right),\left( {\dfrac{{10}}{3},0} \right),\left( {\dfrac{5}{3},\dfrac{8}{3}} \right) \\
$
VerifiedHint: In this question first we need to find at least two points which lie on given lines of triangle y=x, y=0 and 3x+3y=10 to draw their lines on a graph. And then we have to find the intersection points between lines because these intersection points are the coordinates of vertices of the triangle which is formed by given three lines.
Complete step-by-step answer:
We have,
$y = x{\text{ eq}}{\text{.1}} \\
{\text{y = 0 eq}}{\text{.2}} \\
{\text{3x + 3y = 10 eq}}{\text{.3}} \\
$
We know, to draw a line on a graph we require at least two points to join them to form a line .
So first we have to find points on line.
Consider eq.1
$y = x$
Put x=2 then y=2. Therefore, (2,2) lies on the above line.
Again put x=1 then y=1. Therefore, (1,1) lies on the above line.
Now, consider eq.2
y=0
The above equation represents the whole x-axis where y coordinate is zero.
Now, consider eq.3
$3x + 3y = 10$
Now, put x=0 then $y = \dfrac{{10}}{3}$. Therefore,$\left( {0,\dfrac{{10}}{3}} \right)$lies on the above line.
Now, put y=0, then $x = \left( {\dfrac{{10}}{3}} \right)$. Therefore,$\left( {\dfrac{{10}}{3},0} \right)$lies on the above line.
Now, we plot these three lines on graphs using obtained points on their respective lines.
Web know, given lines are sides of triangle it means intersection points of these lines between them gives us the coordinates of vertices of triangle which is formed by given three lines y=x, y=0 and 3x+3y=10
From above graphical representation of lines of triangle the coordinates of vertices of triangle which is formed by the given three lines are \[\left( {0,0} \right),\left( {\dfrac{{10}}{3},0} \right),\left( {\dfrac{5}{3},\dfrac{5}{3}} \right)\].
Hence, option A is correct.
Note: Whenever you get this type of question the key concept to solve this is to learn how to plot a line on a graph when its equation is given using the substitution method. And remember one more thing that to plot a line on a graph at least two points which lie on this line are required.
