Midpoint Formula
In geometry, we all come across the topic of the midpoint formula. It is a very uncomplicated topic to be discussed with you. We all know what line is. A line can be horizontal or vertical. The line can be explained as a straight line drawn by us which is moving endlessly and extending from both sides. A line with two points A and B are called the line segment. A line with one end is called a ray. (diagram 1).
A straight line has no curve. A line has no ends. so here the concept of line is clear, we clear it because the midpoint formula is on the line so for understanding the formula of midpoint we must clear our concepts. Now comes up with midpoint, suppose we draw a line segment with two points O and P. (diagram 2) On the line we mark the point Q in between the line segment which is dividing the line into two equal parts. When we try to find the midpoint in the centre of the line segment or point which is lying in the centre of the line segment. Let’s suppose point Q is dividing a line into r/s (diagram 3). We take (x1, y1) the coordinates of r and (x2, y2) will be the coordinates of s. and we take (x, y) as a coordinate of point Q. With the help of section formula, the x coordinate of point Q will be written as (Diagram 5) and for the y coordinate of a point, Q will be written as (Daigram6).
How to use Midpoint Formula?
On the line segment if we take Q as a midpoint then we say r = s. To get this formula we simply by going ina crossway we easily get the formula for x and y coordinates ( diagram 7,8). We are taking r = s so we put s in place or r we will replace ‘r’ by ‘s’ (diagram 9,10) our numerator and denominator are common, we will cancel out the denominator s by numerator s then we get our x coordinate as x1 + x2 divided by 2. and same we will do with our y coordinate we will cancel the denominator r by numerator r y = y2 + y3 divided by 2. (diagram 11).
we get the coordinates if the midpoint is x1 plus x2 divided by 2, y1 plus y2 divided by 2 (diagram 12). To understand it better we will solve a problem with the help of the formula. On the graph, we draw an x-axis and y-axis. we will find the midpoint between these points (2,2) and (4,5) these are lying on the x and y axes on a drawn graph(diagram 13) the centre of the line is connecting these two points. You can also take a little help from the Mathway Problem solver and can solve any type of question related to mathematics even algebra, calculus, geometry, and some other parts of maths.
By using midpoint formula we will solve it. first, let’s take x1 =2, x2 = 4 same y1 = 2 and y2 = 5. Now put the value into formula 1 + 4 divided by 2 = 2.5 and 2 + 5 divided 2 = 3.5. These points are lying int the centre of the line segment.