Question

Given the points A (3, - 2), B (2, - 5), and C' (4, -5), classify AC.
(1 point)

Answer 1

To classify the segment AC, we first need to find the coordinates of points A and C, which are given as:

- A (3, -2)
- C' (4, -5)

Next, we can find the slope of the line segment AC by using the formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

For points A (3, -2) and C' (4, -5):

- \( x_1 = 3 \)
- \( y_1 = -2 \)
- \( x_2 = 4 \)
- \( y_2 = -5 \)

Substituting these values into the slope formula:

\[
m_{AC} = \frac{-5 - (-2)}{4 - 3} = \frac{-5 + 2}{1} = \frac{-3}{1} = -3
\]

The slope of line segment AC is -3.

To classify segment AC:

- If the slope \( m \) is positive, the line rises from left to right.
- If the slope \( m \) is negative, the line falls from left to right.
- If the slope is zero, the line is horizontal.
- If the slope is undefined, the line is vertical.

Since \( m_{AC} = -3 \), we can classify segment AC as **decreasing** or **falling** since the slope is negative.