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Coordinate Geometry

Question
CBSEENMA10009662

The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, –2). If the third vertex is (7/2, y), find the value of y.

Solution

 Let A(x1, y1)=A(2, 1), B(x2, y2)=B(3,−2) and C(x3, y3)=C(7/2,y).
Area space left parenthesis increment ABC right parenthesis space equals space 1 half vertical line straight x subscript 1 space left parenthesis straight y subscript 2 minus straight y subscript 3 right parenthesis plus straight x subscript 2 left parenthesis straight y subscript 3 minus straight y subscript 1 right parenthesis space plus straight x subscript 3 left parenthesis straight y subscript 1 minus straight y subscript 2 right parenthesis vertical line
rightwards double arrow space 5 space equals space 1 half vertical line 2 left parenthesis negative 2 minus straight y right parenthesis plus 3 left parenthesis straight y minus 1 right parenthesis space plus 7 over 2 left parenthesis 1 plus 2 right parenthesis vertical line
rightwards double arrow 10 space equals space open vertical bar negative 4 minus 2 straight y plus 3 straight y minus 3 space plus 21 over 2 close vertical bar
rightwards double arrow space 10 space equals space open vertical bar straight y plus 7 over 2 close vertical bar
rightwards double arrow space 10 space equals space straight y space plus 7 over 2
or minus 10 space equals space straight y space plus 7 over 2
rightwards double arrow space straight y space equals space 13 over 2 space or space straight y space equals space fraction numerator negative 27 over denominator 2 end fraction