Draw the graphs of the following equations on the same graph paper:$2x\ +\ 3y\ =\ 12$
$x\ -\ y\ =\ 1$
Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis.
Given:
The given equations are:
$2x\ +\ 3y\ =\ 12$
$x\ -\ y\ =\ 1$
To do:
We have to find the coordinates of the vertices of the triangle formed by the given straight lines and the y-axis.
Solution:
To represent the above equations graphically we need at least two solutions for each of the equations.
For equation $2x+3y=12$,
$3y=12-2x$
$y=\frac{12-2x}{3}$
If $x=0$ then $y=\frac{12-2(0)}{3}=\frac{12-0}{3}=\frac{12}{3}=4$
If $x=3$ then $y=\frac{12-2(3)}{3}=\frac{12-6}{3}=\frac{6}{3}=2$
For equation $x-y=1$,
$y=x-1$
If $x=0$ then $y=0-1=-1$
If $x=3$ then $y=3-1=2$
The equationof y-axis is $x=0$.
The above situation can be plotted graphically as below:
The lines AB, CD and AC represent the equations $2x+3y=12$, $x-y=1$ and y-axis respectively.
As we can see, the points of intersection of the lines AB, CD and AC taken in pairs are the vertices of the given triangle.
Hence, the vertices of the given triangle are $(0,4), (0,-1)$ and $(3,2)$.
Related Articles
- Draw the graphs of the following linear equation on the same graph paper.$2x + 3y = 12, x -y = 1$Find the co-ordinates of the vertices of the triangle formed by the two straight lines and the y-axis. Also find the area of the triangle.
- Draw the graphs of the equations $5x – y = 5$ and $3x – y = 3$. Determine the coordinates of the vertices of the triangle formed by these lines and the y-axis.
- Draw the graphs of the equations $x – y + 1 = 0$ and $3x + 2y -12 = 0$. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
- Draw the graph of the pair of equations \( 2 x+y=4 \) and \( 2 x-y=4 \). Write the vertices of the triangle formed by these lines and the \( y \)-axis. Also find the area of this triangle.
- Determine, graphically, the vertices of the triangle formed by the lines $y=x, 3y=x, x+y=8$.
- Draw the graphs of $x\ -\ y\ +\ 1\ =\ 0$ and $3x\ +\ 2y\ -\ 12\ =\ 0$. Determine the coordinates of the vertices of the triangle formed by these lines and x-axis and shade the triangular area. Calculate the area bounded by these lines and x-axis.
- Draw the graphs of the equations $5x\ -\ y\ =\ 5$ and $3x\ -\ y\ =\ 3$. Determine the co-ordinates of the vertices of the triangle formed by these lines and y-axis. Calculate the area of the triangle so formed.
- Draw the graphs of the lines $x=-2$, and $y=3$. Write the vertices of the figure formed by these lines, the x-axis and the y-axis. Also, find the area of the figure.
- Represent the following pair of equations graphically and write the coordinates of points where the lines intersect y-axis$x+3y=6$$2x-3y=12$
- Draw the graphs of the following equations: $2x\ -\ 3y\ +\ 6\ =\ 0$$2x\ +\ 3y\ -\ 18\ =\ 0$$y\ -\ 2\ =\ 0$Find the vertices of the triangle so obtained. Also, find the area of the triangle.
- Solve the following system of linear equations graphically and shade the region between the two lines and x-axis: $2x\ +\ 3y\ =\ 12$ $x\ -\ y\ =\ 1$
- Draw the graph of the equations $x=3, x=5$ and $2x-y-4=0$. Also, find the area of the quadrilateral formed by the lines and the x-axis.
- Graphically, solve the following pair of equations:$2x+y=6$ $2x-y+2=0$ Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.
- Draw the graphs of the pair of linear equations $x-y+2=0$ and $4x-y-4=0$. Calculate the area of the triangle formed by the lines so drawn and the x-axis.
- Determine, graphically, the vertices of the triangle formed by the lines\( y=x, 3 y=x, x+y=8 \)
Kickstart Your Career
Get certified by completing the course
Get Started
To Continue Learning Please Login
Login with Google