SOLUTION: Point A, which is (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of AB?

Question 736111: Point A, which is (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of AB?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let's use C to refer to the point of intersection of the segment AB with the line

. By definition of bisector, point C must be the midpoint of AB, which is to say that the segments AC and CB must be equal in measure. Since

is a vertical line and is given as perpendicular to the line containing the segment AB, the line containing the segment AB must be a horizontal line. Horizontal lines in

have the characteristic that the

-coordinates of every point on the line are equal. Since A and B are both on a horizontal line, and the

-coordinate of point A is 1, the

-coordinate of point B must be 1 as well. Since C is not only an element of the set of ordered pairs that comprise the line that contains the segment AB, it is also an element of the set that comprises the line

. That means that the

-coordinate of point C must be 2 as is the

-coordinate of every point on the line

. Since A and C have identical

-coordinates (for the same reason that A and B have identical

-coordinates), the distance from A to C is quickly calculated by taking the absolute value of the difference between the

-coordinate of point A and the

-coordinate of point C, that is to say

. Since AC and CB are congruent, the distance from C to B must be the same as the distance from A to C, namely 6 units. 6 units to the right of the point

is the point

which is to say

.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

RELATED QUESTIONS
Point A (-4, 1)is in the standard (x,y) coordinate plane. What must be the coordinate of... (answered by richwmiller)

point A (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of (answered by stanbon)

Point A (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of (answered by DrBeeee)

How do you solve: Point A (�4,1) is in the standard (x,y) coordinate plane. What must be (answered by dlam5)

Please help me with this Point A (-4,1) is in the standard (x,y) coordinate plane.... (answered by richwmiller,solver91311,stanbon)

Point A (4,1)is in the standard (x,y) coordinate plane. What must be the coordinates of... (answered by scott8148)

A (5,2) is in the standard (x,y) coordinate place. what must be the coordinates of the... (answered by solver91311)

Point A(-4,1) is in the standard (x,y) coordinate plane. What must be the coordinares of... (answered by solver91311)

Point A (-4,1) IS THE STANDARD (x,y) coordinate plane what must be the coordinate of... (answered by dabanfield)