Points B (x; 3) and A (-2; 1) lie on a straight line perpendicular to the abscissa axis. Find x

B (x; 3) and A (- 2; 1).

If the line on which the points A and B are perpendicular to the abscissa axis, then the x coordinate will always be constant, that is, if point A has x = – 2, then point B also has a coordinate x = – 2. This can be proved using formulas:

AB = √ ((xB – xA) ^ 2 + (yB – yA) ^ 2) =

√ ((x – (- 2)) ^ 2 + (3 – 1) ^ 2) =

√ (x2 + 4x + 8).

The segment AB is equal to yB – yA = 3 – 1 = 2, since it is perpendicular to the abscissa axis.

√ (x ^ 2 + 4x + 8) = 2,

x ^ 2 + 4x + 8 = 4,

x ^ 2 + 4x + 4 = 0,

x = – 2.



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