If the area of the pentagon formed by the vertices A(1,3),B(−2,5),C(−3,−1),D(0,−2) and E=(2,t) is 452sq. units, then possible value(s) of t is/are
A
−1
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B
1
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C
−99
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D
89
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Solution
The correct option is D89 Given vertices of the pentagon are A(1,3),B(−2,5),C(−3,−1),D(0,−2) and E=(2,t)
We know that the area of pentagon ABCDE 452=12∣∣∣x1x2x3x4x5x1y1y2y3y4y5y1∣∣∣⇒452=12∣∣∣1−2−302135−1−2t3∣∣∣⇒452=12|(5+6)+(2+15)+(6+0)+(0+4)+(6−t)|⇒45=|44−t|⇒44−t=±45⇒−t=−44±45∴t=−1,89