Draw the graphs of the following equations:

2*x* − 3*y* + 6 = 0

2*x* + 3*y* − 18 = 0*y* − 2 = 0

Find the vertices of the triangle so obtained. Also, find the area of the triangle.

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#### Solution

The given equations are

2*x* − 3*y* + 6 = 0 ......(i)

2*x* + 3*y* − 18 = 0 ........(ii)

*y* − 2 = 0 ...........(iii)

The two points satisfying (i) can be listed in a table as

x | -3 | 6 |

y | 0 | 6 |

The two points satisfying (ii) can be listed in a table as,

x | 0 | 9 |

y | 6 | 0 |

The two points satisfying (iii) can be listed in a table as,

x | -1 | 8 |

y | 2 | 2 |

Now, graph of equations (i), (ii) and (iii) can be drawn as,

It is seen that the coordinates of the vertices of the obtained triangle are

A(3,4), B(0,2), C(6,2)

∴ Area of ΔABC = 1/2 x Base x height = 1/2 x 6 x 2 sq unit = 6 sq units

Is there an error in this question or solution?

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