If A(x_{1},y_{1}), B(x_{2},y_{2}and C(x_{3}, y_{3}) be three vertices of a ΔABC, then its area is given by:Δ = 1/2 [x_{1}(y_{2}- y_{3}+ x_{2}(y_{3}- y_{1}) + x_{3}(y_{1}- y_{2})]

A.) 29 units | B.) 35.9 sq.units |

C.) 39 sq.units | D.) 39.5 sq.units |

Answer: Option 'C'

Here, x_{1} = 9, x_{2} = 3, x_{3} = -2 and y_{1} = -5, y_{2} = 7, y_{3} = 4

= 1/2 [9(7-4) + 3(4+5) + (-2)(-5-7)]

= 1/2 [9(3) + 3(9) - 2(-12)]

= 1/2 [27 + 27 + 24]

= 1/2 [78]

= 39 sq.units

Here, x

= 1/2 [9(7-4) + 3(4+5) + (-2)(-5-7)]

= 1/2 [9(3) + 3(9) - 2(-12)]

= 1/2 [27 + 27 + 24]

= 1/2 [78]

= 39 sq.units

A.) 9 units | B.) 5 sq.units |

C.) 7 sq.units | D.) 6 sq.units |

Answer: Option 'D'

Here, x_{1} = 2, x_{2} = 4, x_{3} = 6 and y_{1} = -5, y_{2} = 9, y_{3} = -1

= 1/2 [2(9+1) + 4(-1+5) + 6(5-9)]

= 1/2 [2(10) + 4(4) + 6(-4)]

= 1/2 [20 + 16 - 24]

= 1/2 [12]

= 6 sq.units

Here, x

= 1/2 [2(9+1) + 4(-1+5) + 6(5-9)]

= 1/2 [2(10) + 4(4) + 6(-4)]

= 1/2 [20 + 16 - 24]

= 1/2 [12]

= 6 sq.units

A.) equilateral | B.) right angled |

C.) isosceles | D.) scalene |

Answer: Option 'C'

AB^{2}= (-5 - 0)^{2} + (-3 - 0)^{2} = 16 + 9 = 25

BC^{2} = (3 + 5)^{2} + (1-3)^{2} = 8^{2} + (-2)^{2} = 64 + 4 = 68

AC^{2} = (3 - 0)^{2} + (1 - 6)^{2} = 9 + 25 = 34.

AB = AC. ==> ΔABC is isosceles.

AB

BC

AC

AB = AC. ==> ΔABC is isosceles.

A.) An isosceles right angled triangle | B.) An equilateraltriangle |

C.) A scalene triangle | D.) None of these |

Answer: Option 'A'

AB^{2} = (1 + 4)^{2} + (-4 - 0)^{2}

= 25 + 16 = 41,

BC^{2} = (5 - 1)^{2} + (1 + 4)^{2} = 4^{2} + 5^{2}

= 16 + 25 = 41

AC^{2} = (5 + 4)^{2} + (1 - 0)^{2}

= 81 + 1 = 82

AB = BC and AB^{2} = BC^{2} = AC^{2}

ΔABC is an isosceles right angled triangle

AB

= 25 + 16 = 41,

BC

= 16 + 25 = 41

AC

= 81 + 1 = 82

AB = BC and AB

ΔABC is an isosceles right angled triangle

A.) 5 1/2 sq.units | B.) 2 1/3 sq.units |

C.) 2 1/2 sq.units | D.) None of these |

Answer: Option 'C'

Here, x_{1} = 2, x_{2} = -4, x_{3} = 5 and y_{1} = 8, y_{2} = 2, y_{3} = -1

= 1/2 [2(3+1) - 4(-1-8) + 5(8-3)]

= 1/2 [2(4) + 4(-9) + 5(5)]

= 1/2 [16 - 36 + 25]

= 1/2 [5]

= 2 1/2 sq.units

Here, x

= 1/2 [2(3+1) - 4(-1-8) + 5(8-3)]

= 1/2 [2(4) + 4(-9) + 5(5)]

= 1/2 [16 - 36 + 25]

= 1/2 [5]

= 2 1/2 sq.units

Students can learn and improve on their Cognitive and Mathematical Fast Calculation skills and prepare for competitive examinations like...

- All I.B.P.S and Public Sector Bank Competitive Exam
- Common Aptitude Test (CAT) Exams
- UPSC Paper-II or CSAT Exams
- SSC Competitive Exams
- Defence Competitive Exams
- L.I.C / G.I.C AO and Clerk Competitive Exams
- Railway Competitive Exam
- University Grants Commission (UGC)
- Career Aptitude Test (IT Companies) and etc.

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