Write the distance between the points A(10 , 0) and B(0,10 ). - Vidyadip

Question

Write the distance between the points $\text{A}(10\cos\theta, 0)$ and $\text{B}(0,10\sin\theta).$

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Answer

Distance between the points $\text{A}(10\cos\theta, 0)$ and $\text{B}(0,10\sin\theta).$
$=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
$=\sqrt{(0-10\cos\theta)^2+(10\sin\theta-0)^2}$
$=\sqrt{100\cos^2\theta+100\sin^2\theta}$
$=\sqrt{100(\sin^2\theta+\cos^2\theta)}$
$=\sqrt{100\times1}=\sqrt{100}$
$\{\because\ \sin^2\theta+\cos^2\theta=1\}$
$=10$

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