Final answer:
To find the equation for the perpendicular bisector of a line segment, we first need to find the midpoint of the line segment, which can be calculated by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints. The midpoint of the line segment with endpoints (-1, 1) and (-7, -7) is (-4, -3). The slope of the perpendicular bisector is 3/4 and the equation of the perpendicular bisector is y = (3/4)x.
Step-by-step explanation:
To find the equation for the perpendicular bisector of a line segment, we first need to find the midpoint of the line segment, which can be calculated by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints. The midpoint of the line segment with endpoints (-1, 1) and (-7, -7) is (-4, -3).
Next, we need to find the slope of the line segment. The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment. The slope of the line segment is (-7 - 1) / (-7 - (-1)), which simplifies to -8/6 or -4/3.
Since the perpendicular bisector of a line segment has a slope that is the negative reciprocal of the slope of the line segment, the slope of the perpendicular bisector is 3/4. Using the slope-intercept form of the equation of a line (y = mx + b), we can substitute the slope and the coordinates of the midpoint into the equation to solve for b. Plugging in (x, y) = (-4, -3) and m = 3/4, we get -3 = (3/4)(-4) + b. Simplifying this equation gives us b = -3 + 3, or b = 0.
Therefore, the equation of the perpendicular bisector of the line segment with endpoints (-1, 1) and (-7, -7) is y = (3/4)x.