The area of the triangle formed by the points given in the polar co-ordinates $(0, 0), (3, \frac{π}{2})$ and $(5, \frac{π}{3})$ is ______ sq.units.

15

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\frac{15}{2}

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\frac{15}{4}

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\frac{15}{8}

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Solution

The correct option is C $\frac{15}{4}$
Let the points be
$A = (0, 0)$
$B = (3, \frac{π}{2})$
$C = (5, \frac{π}{3})$
In Cartesian form,
using conversion of polar to cartesian ie, x=r.cos(Q) and y=r.sin(Q)
$A = (0, 0)$
$B = (0, 3)$
$C = (\frac{5}{2}, \frac{5 \sqrt{3}}{2})$
Hence by determinant method, we get the area of the triangle as
$= \frac{1}{2} | (\frac{5}{2}) \times 3 |$
$= \frac{15}{4}$ .

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The area of the triangle formed by the points given in the polar co-ordinates (0,0),(3,π2) and (5,π3) is ______ sq.units.

The correct option is C 154Let the points be A=(0,0)B=(3,π2)C=(5,π3)In Cartesian form,using conversion of polar to cartesian ie, x=r.cos(Q) and y=r.sin(Q)A=(0,0)B=(0,3)C=(52,5√32)Hence by determinant method, we get the area of the triangle as =12|(52)×3|=154.

The area of the triangle formed by the points given in the polar co-ordinates $(0, 0), (3, \frac{π}{2})$ and $(5, \frac{π}{3})$ is ______ sq.units.