Point A(-4,1) is in the standard (X,Y) coordinates plane. What must be the coordinates of point B so that the?

Question

line X=2 is the perpedicular bisextor of AB? Please help!

Answer 1

Okay, the line x=2 indicates that it is a vertical line. The slope of a vertical line is always 1/0 which is indefined. it's the simplest form.
So when you know that the slope of the line x=2, then you know the perpendicular slope. it's just the negative reciprical.
But wait, you know that one line is a vertical line, then the perpendicular line must be a horizontal line. The y axis are always the same for any point on a horizontal line. So the y axis of B is 1. So, B is now (x,1)
Then because the line X is the bisector of AB, that means it is in the middle of the whole line. Because we know that the x axis of the the line X is 2, and (2,y) is the midpoint of the AB, then we know that MA is 6 units long. Then we add 2 to 6, 2 as the midpoint and 6 as the length to find the x axis of B, whcih would become 8. So the coordinates of B is (8, 1).

Answer 2

So, the line x=2 is vertical. This means that the point B (x,y) must have the same y-coordine as A (making the slope zero, which it must be).

So far we have (x,1), and we used the "perpendicular" part of the line x=2. For the "bisector" part, the intersection of AB and x=2 (say point C) must divide AB into two equal parts, namely AC and BC.


That means that the horizontal distance (since AB is horizontal) between A and x=2 must equal the horizontal distance between B and x=2.

2-(-4) = 2+4=6

x-2=6
x=8

The pont B has coordinates (8,1)

Hope this helps.

Answer 3

Draw a sketch and the solution will jump at you.

Since x=2 is a vertical line, B must be on a horizontal from A, ie, have the same y coordinate
B(x,1)

now, to get x,
A is 6 units to the left of x=2, thus go 6 units to the right to get B:

B is at (2+6,1) = (8,1).