Identify if line segments AB and CD are perpendicular: 1. $\overline{A B}$ formed by $(-2,13)$ and $(0,3)$ $\overline{C D}$ formed by $(-5,0)$ and $(10,3)$

Step 1 ：We are given two line segments AB and CD. AB is formed by points A(-2,13) and B(0,3), and CD is formed by points C(-5,0) and D(10,3).

Step 2 ：To determine if these line segments are perpendicular, we need to calculate the slopes of the lines AB and CD and check if they are negative reciprocals of each other.

Step 3 ：The slope of a line passing through points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step 4 ：Let's calculate the slope of line AB. For AB, \(x_1 = -2\), \(y_1 = 13\), \(x_2 = 0\), and \(y_2 = 3\). The slope of AB is \(-5.0\).

Step 5 ：Next, let's calculate the slope of line CD. For CD, \(x_1 = -5\), \(y_1 = 0\), \(x_2 = 10\), and \(y_2 = 3\). The slope of CD is \(0.2\).

Step 6 ：Now, we check if the slopes are negative reciprocals of each other. The product of the slopes of AB and CD is \(-5.0 * 0.2 = -1.0\).

Step 7 ：Since the product of the slopes is -1, the lines AB and CD are perpendicular.

Step 8 ：Final Answer: The line segments \(\overline{A B}\) and \(\overline{C D}\) are \(\boxed{perpendicular}\).