Pleas y'all help me with this
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The equation in slope intercept form of a line that is a perpendicular bisector of segment AB with endpoints A(-5,5) and B(3,-3) is y = x + 2
<h3><u>Solution:</u></h3>Given, two points are A(-5, 5) and B(3, -3)
We have to find the perpendicular bisector of segment AB.
Now, we know that perpendicular bisector passes through the midpoint of segment.
<em><u>The formula for midpoint is:</u></em>
<em><u>Finding slope of AB:</u></em>
We know that product of slopes of perpendicular lines = -1
So, slope of AB slope of perpendicular bisector = -1
- 1 slope of perpendicular bisector = -1
Slope of perpendicular bisector = 1
We know its slope is 1 and it goes through the midpoint (-1, 1)
<em><u>The slope intercept form is given as:</u></em>
y = mx + c
where "m" is the slope of the line and "c" is the y-intercept
Plug in "m" = 1
y = x + c ---- eqn 1
We can use the coordinates of the midpoint (-1, 1) in this equation to solve for "c" in eqn 1
1 = -1 + c
c = 2
Now substitute c = 2 in eqn 1
y = x + 2
Thus y = x + 2 is the required equation in slope intercept form