Draw the graph of the pair of equations $2x + y = 4$ and $2x - y = 4$. Write the vertices of the triangle formed by these lines and the $y$-axis. Also,find the area of this triangle.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) The given pair of linear equations are $2x + y = 4$ and $2x - y = 4$.
Table for line $2x + y = 4$:
$x$$0$$2$
$y = 4 - 2x$$4$$0$
Points$A(0, 4)$$B(2, 0)$

Table for line $2x - y = 4$:
$x$$0$$2$
$y = 2x - 4$$-4$$0$
Points$C(0, -4)$$B(2, 0)$

By plotting these points on a graph,we observe that the two lines intersect at point $B(2, 0)$ and intersect the $y$-axis at points $A(0, 4)$ and $C(0, -4)$.
The triangle formed by these lines and the $y$-axis is $\triangle ABC$.
The vertices of the triangle are $A(0, 4)$,$B(2, 0)$,and $C(0, -4)$.
The base of the triangle lies on the $y$-axis,with length $AC = |4 - (-4)| = 8$ units.
The height of the triangle is the perpendicular distance from point $B(2, 0)$ to the $y$-axis,which is $2$ units.
Area of $\triangle ABC = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 2 = 8$ sq units.
Thus,the vertices are $(0, 4), (2, 0), (0, -4)$ and the area is $8$ sq units.

Explore More

Similar Questions

Ankita travels $14 \,km$ to her home partly by rickshaw and partly by bus. She takes half an $hour$ if she travels $2 \,km$ by rickshaw and the remaining distance by bus. On the other hand,if she travels $4 \,km$ by rickshaw and the remaining distance by bus,she takes $9 \,minutes$ longer. Find the speed of the rickshaw and of the bus (in $km/h$).

Difficult
View Solution

The diagram given below shows two sticks $-$ one $BLACK$ and the other $WHITE$. Based on the measurements shown,what is the length of the white stick? (in $cm$)

Difficult
View Solution

In the pair of linear equations $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,if $\ldots \ldots \ldots \ldots$,then the system has infinitely many solutions.

By the graphical method,find whether the following pair of equations are consistent or not. If consistent,solve them.
$x - 2y = 6$
$3x - 6y = 0$

The age of the father is twice the sum of the ages of his two children. After $20$ years,his age will be equal to the sum of the ages of his children. Find the age of the father (in years).

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo