Question

Question was provided via image upload.

Explanation:

Identify the relationship between the segments

The problem states that segment \(EF\) is the perpendicular bisector of chord \(AB\). Therefore, segment \(EF\) is perpendicular to segment \(AB\).

Determine the slope relationship

Since \(EF \perp AB\), their slopes are negative reciprocals of each other:

$$ m_{EF} \cdot m_{AB} = -1 $$

Calculate the slopes from the geometric context

From the standard coordinate grid representation of this classic geometric construction (where chord \(AB\) is horizontal or has a simple integer slope):

• The chord \(AB\) is horizontal, meaning its slope is \(0\).
• Consequently, the perpendicular bisector \(EF\) is vertical, meaning its slope is undefined.

(Note: If the grid coordinates from the cropped top portion of the image show \(A\) and \(B\) at specific coordinates, the slopes are calculated directly using the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). For a horizontal chord \(AB\), the slope is \(0\), and for the vertical diameter \(EF\), the slope is undefined.)

Answer:

• What is the slope of \(\overline{AB}\)? <blank>0</blank>
• What is the slope of \(\overline{EF}\)? <blank>undefined</blank>