Question

the coordinates of the endpoints of the line segment ab are a(0,5) and b(10,5). what is the equation of the line perpendicular to ab passing through its midpoint? 1 ( x = 5 ) 2 ( x = 10 ) 3 ( y = 10 ) 4 ( y = 5 )

Explanation:

Step1: Find the slope of AB

The coordinates of A are (0, 5) and B are (10, 5). The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the values, we get $m = \frac{5 - 5}{10 - 0} = \frac{0}{10} = 0$. So, line AB is horizontal (since slope is 0).

Step2: Determine the slope of the perpendicular line

A line perpendicular to a horizontal line is vertical. The slope of a vertical line is undefined.

Step3: Find the midpoint of AB

The midpoint formula is $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$. Substituting the coordinates of A and B, we get $(\frac{0 + 10}{2}, \frac{5 + 5}{2}) = (5, 5)$.

Step4: Find the equation of the perpendicular line

A vertical line passing through (5, 5) has the equation $x = 5$ (since for a vertical line, the x - coordinate is constant for all points on the line).

Answer:

1. \( x = 5 \)