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Determinants

Question
CBSEENMA12034493
Wired Faculty App

Find the value of x if the area of triangle is 35 square cm. with vertices (x, 4), (2, – 6) and (5, 4).

Solution

Since area of triangle formed by the points (x , 4), (2, – 6). (5, 4) is 35 sq. cm.
therefore space space space space 1 half open vertical bar table row straight x cell space space space space 4 end cell cell space space 1 end cell row 2 cell space space minus 6 end cell cell space space 1 end cell row 5 cell space space 4 end cell cell space space 1 end cell end table close vertical bar space equals space plus-or-minus 35 space space space space space space space space space space space space space space space space space space space rightwards double arrow space open vertical bar table row straight x cell space space space 4 end cell cell space space 1 end cell row 2 cell space minus 6 end cell cell space space 1 end cell row 5 4 cell space space 1 end cell end table close vertical bar space equals space plus-or-minus 70 rightwards double arrow space space space space space space straight x open vertical bar table row cell negative 6 end cell cell space space space 1 end cell row 4 cell space space space 1 end cell end table close vertical bar minus 4 space open vertical bar table row 2 cell space space space space 1 end cell row 5 cell space space space space 1 end cell end table close vertical bar plus space 1 space open vertical bar table row 2 cell negative 6 end cell row 5 4 end table close vertical bar space equals space plus-or-minus 70 rightwards double arrow space space space space space left parenthesis negative 6 minus 4 right parenthesis straight x minus 4 left parenthesis 2 minus 5 right parenthesis plus 1 left parenthesis 8 plus 30 right parenthesis space equals space plus-or-minus 70 rightwards double arrow space space space space minus 10 straight x plus 12 plus 38 space equals space plus-or-minus 70 space space space space space space space space space space space space rightwards double arrow space space space 10 straight x space equals space 20 comma space space space minus 120 space space space rightwards double arrow space space straight x space equals space 2 comma space minus 12.

Tips: -

Whenever area of a triangle is given, ± sign should be taken.

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