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The coordinate of point $R$on a line is $8$, the point $S$ is on the same line which is to the left of $R$ and a distance of $7$ units from $R$. Find the coordinate of $S$. If $P$ is the midpoint of seg $RS$, find the coordinate point $P$.
A. Coordinate of$S$ is $0$. $P\leftrightarrow 3$
B. Coordinate of$S$ is $1$. $P\leftrightarrow 3.5$
C. Co-ordinate of$S$ is $2$. $P\leftrightarrow 34$
D. Coordinate of$S$ is $4$. $P\leftrightarrow 5$

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Last updated date: 24th Jul 2024
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Answer
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Hint: To solve this question, we will draw a graph of the number line for all the given statements in the question with respective given numbers. Then, we will combine them one until we get the final graph of the number line with all the points. In between we will use the formula of midpoint to get the required value of that is $P$, $\text{midpoint = }\dfrac{\text{distance between two points}}{\text{2}}$.

Complete step-by-step solution:
Since, the first statement states that the coordinate of point $R$on a line is $8$. So, we will draw graph according to this statement as:
seo images

Now, we will use the statement to draw further graph that says the point $S$ is to the left of $R$ and at a distance of $7$ units from $R$ as:
seo images

 Since, $P$ is the midpoint of seg $RS$ and we already have the distance between $R$ and $S$. So, the coordinates of the point $P$ will be calculated by the formula of midpoint.
$\Rightarrow \text{midpoint = }\dfrac{\text{distance between two points}}{\text{2}}$
Substitute the distance between the seg $RS$ that is $7$ in the above formula as:
$\Rightarrow \text{midpoint = }\dfrac{\text{7}}{\text{2}}$
After solving above step, we will have:
$\Rightarrow \text{midpoint = 3}\text{.5}$
So, the coordinate of point $P$ is $3.5$ and the related graph is:
seo images

Hence, the option \[~\text{B}\] is the correct answer.

Note: The coordinate of a point on a number line is a real number or the real number presents the coordinate of a point on a number line by itself. Here we have taken the number line for representing the numbers. Some students make mistakes by considering the coordinate term as geometry coordinates which will lead to the wrong answer. So we need to take care of this point.