Question

plot point c(1, 0).
use the segment tool to draw radius $overline{ac}$.
draw the line that is tangent to circle a and goes through point c.
use the slope tool to determine the slopes of radius $overline{ac}$ and the tangent line that it intersects.
type the correct answer in each box. use numerals instead of words.
the slope of radius $overline{ac}$ is
the slope of the tangent line is

Explanation:

To solve this, we assume the center of the circle \( A \) is at the origin \((0,0)\) (since the problem involves a radius \( \overline{AC} \) with \( C(1,0) \), a common setup).

Step 1: Slope of Radius \( \overline{AC} \)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
For points \( A(0,0) \) and \( C(1,0) \):
\[
m_{\overline{AC}} = \frac{0 - 0}{1 - 0} = \frac{0}{1} = 0
\]

Step 2: Slope of Tangent Line at \( C \)

A tangent to a circle is perpendicular to the radius at the point of tangency.
If two lines are perpendicular, the product of their slopes is \( -1 \). Let the slope of the tangent be \( m_t \).
We know \( m_{\overline{AC}} = 0 \) (a horizontal line). A line perpendicular to a horizontal line is vertical, which has an undefined slope (or mathematically, the slope of a vertical line is \( \frac{1}{0} \), which is undefined).

Answer:

s:
The slope of radius \( \overline{AC} \) is \( \boldsymbol{0} \).
The slope of the tangent line is \( \boldsymbol{\text{undefined}} \) (or represented as no finite number, but in the context of perpendicularity to a horizontal line, it’s a vertical line with undefined slope).