Question

Determine graphically the vertices of the triangle formed by lines 2x+3y=12 ,x-y-1=0 and x=0. Also find the area of the triangle. ​

Answer 1

Answer:

(0, 4), (3, 2), (0, -1) A = 7.5 unit^2

Step-by-step explanation:

Answer 2

We form $\Delta ABC$ whose sides are

$\quad AB:2x+3y=12$

$\quad BC:x=0$

$\quad CA:x-y=1$

FINDING THE VERTICES:

The coordinates of the vertex $B$:

The vertex $B$ is formed by the sides $AB$ and $BC$.

1. Draw the side AB:

$\begin{array}{ccc}x\to&0&3\\y\to&-1&2\end{array}$

Plot the points $(0,\:-1)$, $(3,\:2)$ and draw the side $AB$.

2. Draw the side BC:

Clearly $BC$ is the $y-$ axis.

• The intersection of $AB$ and $BC$ is the point $B\:(0,\:4)$.

The coordinates of the vertex $C$:

The vertex $C$ is formed by the sides $BC$ and $CA$.

1. Draw the side $BC$:

Clearly $BC$ is the $y-$ axis.

2. Draw the side $CA$:

$\begin{array}{ccc}x\to&0&1\\y\to&-1&0\end{array}$

Plot the points $(0,\:-1)$, $(1,\:0)$ and draw the side $CA$.

• The intersection of $BC$ and $CA$ is the point $C\:(0,\:-1)$.

The coordinates of the vertex $A$:

The vertex $A$ is formed by the sides $AB$ and $CA$.

1. Draw the side $AB$:

$\begin{array}{ccc}x\to&0&3\\y\to&-1&2\end{array}$

Plot the points $(0,\:-1)$, $(3,\:2)$ and draw the side $AB$.

2. Draw the side $CA$:

$\begin{array}{ccc}x\to&0&1\\y\to&-1&0\end{array}$

Plot the points $(0,\:-1)$, $(1,\:0)$ and draw the side $CA$.

• The intersection of $AB$ and $CA$ is the point $A\:(3,\:2)$.

Answer: The vertices of $\Delta ABC$ are $A\:(3,\:2)$, $B\:(0,\:4)$ and $C\:(0,\:-1)$.

AREA OF THE TRIANGLE:

The base of $\Delta ABC$ is $BC$ and the height is $AD$.

$\quad\quad BC=5\:units$

$\quad\quad AD=3\:units$

Therefore the required area is

$\quad=\frac{1}{2}\times base\times height$

$\quad=\frac{1}{2}\times 5\times 3\:unit^{2}$

$\quad=7.5\:unit^{2}$

Answer: The area of the given triangle is $7.5\:unit^{2}$.