Question

Find the general equation of the perpendicular bisector of line segment AB if A is (-3,1) and B is (5,2).

Answer 1

The general equation of the perpendicular bisector of line segment AB with endpoints A (-3,1) and B (5,2) is 8x + y - 9.5 = 0.

Step-by-step explanation:

To find the general equation of the perpendicular bisector of line segment AB with points A (-3,1) and B (5,2), we follow a series of steps:

1. First, calculate the midpoint of AB, which will be a point on the bisector.
2. Then, find the slope of AB and determine the negative reciprocal (since the bisector is perpendicular).
3. Using the midpoint and the slope of the bisector, write the equation in point-slope form.
4. Finally, convert this equation to the general form.

Let's consider components and slope calculations:

• The midpoint is ((-3+5)/2, (1+2)/2) which simplifies to (1, 1.5).
• The slope of AB is (2-1)/(5+3), which equals 1/8.
• The slope of the perpendicular bisector is the negative reciprocal, -8.
• The point-slope form with the midpoint is y - 1.5 = -8(x - 1).
• Rearranging to general form: 8x + y = 8 + 1.5 = 9.5, or 8x + y - 9.5 = 0.

The general equation of the perpendicular bisector for the line segment AB is 8x + y - 9.5 = 0.