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Question 257290: Point A (-4,1) IS THE STANDARD (x,y) coordinate plane what must be the coordinate of point B so that the line x-2 is the perpendicular bisector of AB
Answer by dabanfield(803)   (Show Source):
You can put this solution on YOUR website! Point A (-4,1) IS THE STANDARD (x,y) coordinate plane what must be the coordinate of point B so that the line x-2 is the perpendicular bisector of AB
The line y = x - 2 is in slope-intercept form so has a slope of 1. The line passing througth (-4,1) which is perpendicular to this line must have a slope which is the negative reciprocal of 1 which is -1/1 = -1.
So the equation of the perpendicular line in slope-intercept form is
y = -1*x + b
Since (-4,1) is on this line we have:
1 = -1*-4 + b
b = -3
The equation of the perpendicular line is then:
y = -x - 3
To see where the two lines intersect we need to simulaneously solve:
1.) y = -x - 3
2.) y = x - 2
Substitute x-2 in equation 1.):
x - 2 = -x - 3
2x = -1
x = -1/2 (the x-coordinate of B)
Substitute -1/2 for x in 2.) above to get the value of y for point B.
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