Question

select the correct answer from each drop - down menu. segment pr is tangent to circle c at point q. the slope of cq is -1/2. the measure of ∠cqp is the slope of pr is

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\angle CQP = 90^{\circ}$.

Step2: Recall slope of perpendicular lines

If the slope of a line $l_1$ is $m_1$ and the slope of a line $l_2$ perpendicular to it is $m_2$, then $m_1\times m_2=- 1$. Given $m_1 =-\frac{1}{2}$ for $\overline{CQ}$, let the slope of $\overline{PR}$ be $m_2$. Then $-\frac{1}{2}\times m_2=-1$. Solving for $m_2$ gives $m_2 = 2$.

Answer:

The measure of $\angle CQP$ is $90^{\circ}$.
The slope of $\overline{PR}$ is $2$.