Question

Let A(0,6), B(1,2), C(3,3), D(3,2), and E(4,2) be given points, then which of the following is (are) true?

A
Area of pentagon formed by these points is 732
B
Area of triangle formed by points below x-axis is 12 square units
C
Angle subtended by BD at A is tan13261
D
All of these
Solution
Verified by Toppr

Given the points
A(0,-6), B(1,2), C(3,-3),D(-3,2) and E(-4,-2)
Area of the pentagon = Area formed by a polygon =
(x1y2y1x2)+(x2y3y2x3)...+(xny1ynx1)2
where a1 is the coordinate of vertex 1 and yn is the y-coordinate of the nth vertex etc.
Area ∣ ∣ ∣ ∣[(3×2)(2×1)]+[(1×3)(3×2)]+[(3×6)(3×0)]+[(4×2)(2×3)]+[(0×2)(6×4)]2∣ ∣ ∣ ∣=732=732
Area of triangle formed by points below $x-axis,
Area=12bh=×6=242=12 square unit
Angle subtended by BD at A=tan1(8261)

892591_296435_ans_b17ce50ae0b64d5cbd071b1f0c0976af.png

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