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

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

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