Question

What is the perpendicular distance of point \[\left( {4,3} \right)\] from x- axes.

Answer 1

Hint: First we need to recognize or identify the x and y coordinates from a given point. The x-coordinate of the given point is the perpendicular distance of the given point from the y-axis. The y-coordinate of the given point is the perpendicular distance of the given point from the x-axis.

Complete step by step answer:
 Let \[p\left( {x,y} \right)\] be any point, since the perpendicular distance from y-axis to a point \[p\left( {x,y} \right)\] is x-coordinate value and also distance is always positive quantity, Hence, \[\left| x \right|\] is the distance.
Similarly, the perpendicular distance from x-axis to a point\[p\left( {x,y} \right)\]  is y-coordinate
Value. Hence, \[\left| y \right|\] is the distance.
In a given point \[\left( {4,3} \right)\], x-coordinate is \[4\] and y-coordinate is \[3\].
Also, the absolute values of x and y coordinates are \[4\]and \[3\] respectively.
The point \[\left( {4,3} \right)\] is located in the coordinate plane as shown in the graph below.

clearly, the perpendicular distance from y-axis to a point\[\left( {4,3} \right)\] is \[4\] and the perpendicular distance from x-axis to a point\[\left( {4,3} \right)\] is \[3\].
Hence the perpendicular distance of point \[\left( {4,3} \right)\] from x-axes is \[3\]units.

Note:
Note that the lines which are perpendicular to the x-axis are all parallel to the y-axis and they are also known as vertical lines. The lines which are perpendicular to the y-axis are all parallel to the x-axis and they are also known as horizontal lines.
The abscissa of any point \[\left( {x,y} \right)\] is x-coordinate and the ordinate of any point \[\left( {x,y} \right)\] is y-coordinate. We use “abscissa” and “ordinate” terms in the solution.