Given A (-3,1) to origin to C (1,3). How do you measure that angle?

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Answer 1 · 2016-08-16T16:47:57

$m ∠ A O C = \frac{π}{2}$ $m/_AOC=pi/2$ .

$A (- 3, 1), C (1, 3)$ $A(-3,1), C(1,3)$ are given pts. and we require the measure of

$∠ A O C$ $/_AOC$ , i.e., $m ∠ A O C$ $m/_AOC$ , where, $O$ $O$ is the Origin, $O (0, 0)$ $O(0,0)$

Let the slope of line $O A$ $OA$ be $m_{1}$ $m_1$ , and, $m_{2}$ $m_2$ that of line $O C$ $OC$ .

Then, $m_{1} = \frac{1 - 0}{- 3 - 0} = - \frac{1}{3}, and, m_{2} = \frac{3 - 0}{1 - 0} = 3$ $m_1=(1-0)/(-3-0)=-1/3, and, m_2=(3-0)/(1-0)=3$ .

Hence, $m_{1} \cdot m_{2} = (- \frac{1}{3}) (3) = - 1$ $m_1*m_2=(-1/3)(3)=-1$

$\Rightarrow O A ⊥ O C$ $rArr OA bot OC$

$m ∠ A O C = \frac{π}{2}$ $m/_AOC=pi/2$ .