Maths / Coordinate Geometry / Area of Triangle Using Coordinate

QUESTION
 

The area of the triangle formed by the points (k - 1 , k + 1) ,  (k + 3 , k - 3 ) and ( k + 1 , k + 2) is

OPTIONS
A. 

2 sq units

B. 

3 sq units

C. 

3 k sq. units

D. 

None of these

Right Option : D

EXPLANATION
Explain TypeExplanation Content
Text

The points are ( k-1, k+1), ( k+3, k-3) and (k+1, k+2)

So, area of triangle

=frac {1}{2}left | (k-1)left [ (k-3)-(k+2) right ]+(k+3) left [ (k+2)-(k+1) right ]+(k+1)left [ (k+1)-(k-3) right ]right |

=frac {1}{2}left | (k-1)(-5)+(k+3)(1)+(k+1)(4) right |

=frac {1}{2}left | -5k+5+k+3+4k+4 right |

=frac{1}{2}times 12=6sq: : units.

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