Question

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

Answer 1

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.