Maths / Coordinate Geometry / Area of Triangle Using Coordinate

QUESTION
 

Find the area of the triangle formed by the points A ( 5,2), B (4,7) and C (7,-4).

EXPLANATION
Explain TypeExplanation Content
Text

Here, x_1=5,y_1=2,x_2=4,y_2=7,x_3=7: : and : : y_3=-4

therefore        Area of  Delta ABC=frac {1}{2}left | x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2) right |

Rightarrow         Area of  Delta ABC=frac {1}{2}left | 5(7+4)+4(-4-2)+7(2-7) right |

Rightarrow      Area of Delta ABC=frac {1}{2}left | (5times11+4times(-6)+7times-5) right |

Rightarrow      Area of  Delta ABC=frac {1}{2}left | (55-24-35) right |=frac {1}{2}left | -4 right |=2sq. units.

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