Question

Construct a line from A perpendicular to the x-axis, determine the distance from A to the x-axis along this perpendicular line, find a new point on the other side of the x-axis that is equidistant from the x-axis.

Answer 1

Step-by-step explanation:

To determine distances, we need to use this formula: $d=\sqrt{(y_{2}-y_{1} ) ^{2} +(x_{2}-x_{1})  ^{2} }$

To apply that formula we need to use the coordinates of point, but in this case will be calculated generally, due to the lack of specific values.

So, Point A have the coordinates $(x_{1};y_{1})$

Let's call Point P the one that's on the x-axis, its coordinates are $(p_{1};q_{1})$

Applying the formula, the distance between this two points will be:

$d=\sqrt{(q_{1}-y_{1} ) ^{2} +(p_{1}-x_{1})  ^{2} }$

To find an opposite and equidistant point, we only need to use opposite values. So, let's call Point B, the opposite point, its coordinates will be:

$(-x_{1};-y_{1})$

And the distance will be the same, because squared values will always results positive.