Question

The perpendicular distance from point \[\left( {3,4} \right)\] from the $y$ axis is __ units.

Answer 1

Hint: In the coordinate system, there are two axes, $x$ axis and $y$ axis and these are perpendicular to each other. Any coordinate in the $xy$ plane is written as $\left( {{x_1},{y_1}} \right)$ where $\left| {{x_1}} \right|$ is the perpendicular distance to $y$ axis and $\left| {{y_1}} \right|$ is perpendicular distance to $x$ axis.

Complete step-by-step answer:
The number \[\left( {3,4} \right)\] are the coordinates in the coordinate system.
In the coordinate system, there are two axes perpendicular to each other forming a Cartesian plane.
Any coordinate in the $xy$ plane is written as $\left( {{x_1},{y_1}} \right)$ where ${x_1}$ known as the $x$- coordinate and ${y_1}$ is known as the $y$ coordinate.
Also, in the coordinate $\left( {{x_1},{y_1}} \right)$ , $\left| {{x_1}} \right|$ represents perpendicular distance from $y$ axis and $\left| {{y_1}} \right|$ represents perpendicular distance from $x$-axis.
Therefore in coordinate \[\left( {3,4} \right)\], 3 units is the perpendicular distance from $y$- axis and 4 units is the perpendicular distance from $x$-axis.
Hence, the perpendicular distance from the point \[\left( {3,4} \right)\] from $y$-axis is 3 units.

Note:- Many students make mistakes in writing 3 units as perpendicular distance from $x$-axis which is incorrect, 3 is the $x$- coordinate in the ordered pair \[\left( {3,4} \right)\]. The distance from origin can also be calculated using Pythagoras theorem.