2. Mid-point of a line segment

In a kitchen, the gas stove is placed precisely in between the kitchen door and the refrigerator.

 

Since the gas stove is placed right in the middle, the distance between the kitchen door and the gas stove equals the distance between the gas stove and the refrigerator.

 

 

 

From the image given above, it is understood that distance \(1\) equals distance \(2\).

 

\(\text{Distance}\) \(1 =\) \(\text{Distance}\) \(2\)

 

Both the distances(Distance \(1\) and Distance \(2\)) are equal as the gas stove is placed in the mid-point of the distance between the kitchen door and the fridge.

 

 

Mid-point:

Let the end points of a line segment be \(A\) and \(B\), and let the vertices be \((p_1\), \(0)\) and \((p_2\), \(0)\) respectively such that \(p_2 > p_1\).

 

Let \(M\) be the mid-point of the line segment.

 

 

 

 

It is known that \(AM = MB\).

 

Let \(p\) be the vertex of \(M\).

 

Since, \(AM = MB\)

 

\(p - p_1 = p_2 - p\)

 

\(2p = p_1 + p_2\)

 

\(p = \frac{p_1 + p_2}{2}\)