Final answer:
The midpoint of AB is (8, 5). The equation of the line passing through the midpoint and perpendicular to AB is y - 5 = (-3/4)(x - 8).
Step-by-step explanation:
The coordinates of point A are (5, 1) and the coordinates of point B are (11, 9). To find the midpoint of AB, you can use the midpoint formula:
((x1 + x2)/2, (y1 + y2)/2) is the midpoint.
When we enter A and B's coordinates into the formula, we obtain:
Midpoint = ((5 + 11)/2, (1 + 9)/2) = (8, 5)
Now, to find the equation of the line that passes through the midpoint and is perpendicular to AB, we need to determine the slope of AB. The slope of AB is given by:
Slope = (y2 - y1)/(x2 - x1)
When we enter A and B's coordinates into the formula, we obtain: Slope = (9 - 1)/(11 - 5) = 8/6 = 4/3
Since the line we are looking for is perpendicular to AB, its slope is the negative reciprocal of the slope of AB, which is -3/4.
Therefore, the equation of the line passing through the midpoint (8, 5) and perpendicular to AB is y - 5 = (-3/4)(x - 8).