Maths-
General
Easy

Question

The area of triangle with vertices at (–4, –1) , (1, 2), (4, –3)

  1. 12 sq. units    
  2. 18 sq. units    
  3. 17 sq. units    
  4. 30 sq. units    

The correct answer is: 17 sq. units


    G i v e n space c o minus o r d i n a t e s space o f space t h e space t r i a n g l e space a r e
open parentheses x subscript 1 comma space y subscript 1 close parentheses space equals space open parentheses negative 4 comma negative 1 close parentheses
open parentheses x subscript 2 comma space y subscript 2 close parentheses space equals open parentheses 1 comma space 2 close parentheses
open parentheses x subscript 3 comma space y subscript 3 close parentheses space equals open parentheses 4 comma space minus 3 close parentheses
A r e a space o f space a space t r i a n g l e space equals space 1 half left parenthesis x 1 left parenthesis y 2 minus y 3 right parenthesis plus x 2 left parenthesis y 3 minus y 1 right parenthesis plus x 3 left parenthesis y 1 minus y 2 right parenthesis right parenthesis space o r space 1 half open vertical bar table row cell open parentheses x subscript 1 space minus space x subscript 2 close parentheses space end cell cell open parentheses y subscript 1 space minus space y subscript 2 close parentheses space end cell row cell open parentheses x subscript 1 space minus space x subscript 3 close parentheses end cell cell open parentheses y subscript 1 space minus space y subscript 3 close parentheses end cell end table close vertical bar
therefore text Area  end text equals 1 half open vertical bar table row cell left parenthesis negative 4 minus 1 right parenthesis blank left parenthesis negative 1 minus 2 right parenthesis end cell row cell left parenthesis negative 4 minus 4 right parenthesis blank left parenthesis negative 1 plus 3 right parenthesis end cell end table close vertical bar equals 1 half open vertical bar table row cell negative 5 end cell cell negative 3 end cell row cell negative 8 end cell 2 end table close vertical bar equals 1 half vertical line minus 10 minus 24 vertical line equals 17 text  sq.units end text

    Here, the area of a triangle cannot be negative. Hence only the numerical value is considered.

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