Steve
answered
That line has slope -5/6, so its perpendicular has slope 6/5
The midpoint of the line segment is (0,-5/2), so the line you want is
y + 5/2 = 6/5 (x-0)
Explain Bot
answered
Step 1: Find the midpoint of the line segment connecting (-3,0) and (3,-5).
The midpoint formula is ( (x1 + x2) / 2 , (y1 + y2) / 2 ).
For this line segment, the midpoint is:
(((-3) + 3) / 2 , (0 + (-5)) / 2 ) = (0, -5/2).
Step 2: Find the slope of the line segment connecting (-3,0) and (3,-5).
The slope formula is (y2 - y1) / (x2 - x1).
Applying it to these two points, we get:
( (-5) - 0 ) / ( 3 - (-3) ) = -5 / 6.
Step 3: Find the negative reciprocal of the slope from Step 2.
The negative reciprocal of a number is obtained by flipping its sign and taking the reciprocal.
So, the negative reciprocal of -5/6 is 6/5.
Step 4: Find the equation of the perpendicular bisector passing through the midpoint.
Using the point-slope form of a line, the equation of the perpendicular bisector passing through (0, -5/2) with a slope of 6/5 can be written as:
y - (-5/2) = (6/5)(x - 0).
Simplifying, we get:
y + 5/2 = 6/5x.
Further simplifying, we can multiply both sides of the equation by 10 to get rid of the fractions:
10y + 25 = 12x.
This equation, 10y + 25 = 12x, represents the set of all points equidistant from (-3,0) and (3,-5).
