Question

What is the equation of a perpendicular bisector of the line segment ab where a(-2,1) and b(4,3)?

1) y = -1/3x - 5/3
2) y = -3x + 5
3) y = 3x - 5
4) y = -1/3x + 5/3

Answer 1

The equation of the perpendicular bisector of the line segment AB with endpoints A(-2,1) and B(4,3) is y = -3x + 5.

Step-by-step explanation:

To find the equation of the perpendicular bisector of the line segment connecting points A(-2,1) and B(4,3), we first need to determine the midpoint of the segment and the slope of the perpendicular line. The midpoint (M) can be found using the formula: M = ((x1+x2)/2, (y1+y2)/2), which gives us M = ((-2+4)/2, (1+3)/2) or M = (1, 2). The slope of AB is calculated as (y2-y1)/(x2-x1), which is (3-1)/(4-(-2)) or 2/6, simplified to 1/3. A line perpendicular to AB would have a slope that is the negative reciprocal of AB's slope, which is -3. Using the point-slope form of the equation of a line (y - y1) = m(x - x1), we have y - 2 = -3(x - 1). By expanding and rearranging this equation, we get y = -3x + 5, which is the equation for the perpendicular bisector.