Answer:
-0.4x + y = 2
Explanation:
To find an equation for the perpendicular bisector of the line segment whose endpoints are (-7, -3) and (-3, 7), you can start by finding the midpoint of the line segment. The midpoint is the point on the line segment that is exactly halfway between the two endpoints.
To find the midpoint of the line segment, you can average the x-coordinates and y-coordinates of the two endpoints:
Midpoint: ((-7 + -3)/2, (-3 + 7)/2)
= (-5, 2)
Then, you can find the slope of the line segment by using the formula:
slope = (y2 - y1)/(x2 - x1)
= (7 - (-3))/(-3 - (-7))
= 10/4
= 2.5
The slope of the perpendicular bisector will be the negative reciprocal of the slope of the line segment. To find the slope of the perpendicular bisector, you can take the negative reciprocal of the slope of the line segment:
Perpendicular slope = -1/slope
= -1/(2.5)
= -0.4
Then, you can use the midpoint and the slope of the perpendicular bisector to find the equation of the perpendicular bisector. The equation of a line in slope-intercept form is:
y = mx + b
Where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.
To find the y-intercept of the perpendicular bisector, you can substitute the coordinates of the midpoint and the slope into the equation:
y = (-0.4)x + b
2 = (-0.4)(-5) + b
2 = 2 + b
b = 0
Therefore, the equation of the perpendicular bisector in slope-intercept form is:
y = (-0.4)x + 0
= (-0.4)x
Alternatively, you can write the equation in standard form, which is:
Ax + By = C
Where A, B, and C are constants and x and y are variables. To find the equation of the perpendicular bisector in standard form, you can substitute the slope and the coordinates of the midpoint into the standard form equation:
(-0.4)x + y - 2 = 0
-0.4x + y = 2
Therefore, the equation of the perpendicular bisector in standard form is:
-0.4x + y = 2