Question

The point \[(2k – 8,\ 10)\] lies on y axis . find the value of \[k\] ?

Answer 1

Hint: In this question, we need to find out the value of \[k\] in the point \[(2k – 8,\ 10)\] and also given that the point lies on y axis. Here we will use the concepts of the Cartesian plane that if the point lies on the y axis then the x value of the given point must be zero. First we can consider any point on the y axis to be \[(0,\ n)\] where \[n\] is any integer. Then on equating the point and simplifying , we can get the value of \[k\].

Complete step by step solution:
Given the point \[(2k – 8,\ 10)\] lies on y axis.
Here we need to find the value of \[k\].
Given that the point lies on y axis. We need to know that if the point lies on the y-axis then the x value of the given point must be zero.
Let us consider any point on the y axis be \[(0,\ n)\] where \[n\] is any integer.
Since the point on the y axis is \[(0,\ n)\] , it follows as
\[(0,\ n)\ = \ (2k – 8,\ 10)\]
On equating both the points,
We get,
\[\Rightarrow \ 0 = 2k – 8\] and \[n = 10\]
Now we need to find the value of \[k\],
\[\Rightarrow \ 0 = 2k – 8\]
On rewriting the terms,
We get,
\[\Rightarrow 2k = 8\]
On dividing both sides by \[2\] ,
We get,
\[\Rightarrow \ k = \dfrac{8}{2}\]
On simplifying,
We get,
\[\Rightarrow \ k = 4\]
Thus we get the value of \[k\] as \[4\] .
The value of \[k\] as \[4\] .

Note:
In order to solve these types of questions , we must know the orientation of all the axes. The horizontal axis is often called the x axis and the vertical axis is called the y axis. The upper region is known as the positive y axis whereas the lower region is known as the positive y axis. The leftmost part is known as the positive x axis whereas the rightmost part is known as the positive x axis. It is important to remember that if x coordinate of a point is zero then that point lies on the y axis and if y coordinate of a point is zero then that point lies on the x axis.