Answer:
The y-coordinate of the midpoint = (-3+1)/2 = -2/2 = -1.
2. Calculate the slope of the line segment:
The slope of a
line passing
through two
Step-by-step explanation:
2. Calculate the slope of the line segment:
The slope of a
line passing
through two points can be found using the formula: slope = (change in y-coordinates)/ (change in x-coordinates). For the given points (5, -3) and (-1, 1), the slope can be calculatedas:
slope = (1 - (-3))/ ((-1) - 5) = 4/(-6) = -2/3.
3. Find the negative reciprocal of the slope:
The
perpendicularbisector of a line segment has a slope that is the negative reciprocal of the original line segment. - To find the reciprocal, we flip
negative
the fraction andchange the sign. - The negative reciprocal of -2/3 is 3/2.
4. Use the midpoint and the negative reciprocal slope to find the equation of theperpendicular
bisector: We can use the point-slope form of a linear equation, which is: y-y1=m(x-x1), where (x1, y1) is a point on the line and m is the slope.
Using themidpoint (2, -1) and the negative reciprocal slope 3/2, we can write the equation of the perpendicular bisector: - y - (-1) = (3/2)(x -
2)
Simplifying the equation, we get:- y + 1 = (3/2)(x - 2)
Therefore, the equation of the perpendicular bisector of the segment joining (5, -3) and (-1, 1) is y + 1 = (3/2)(x - 2).
