What is the Midpoint Formula What is the Midpoint Formula Geometry is the very important branch of mathematics and also plays a vital role in the area of mathematics. In the geometry we find mean, median and many things. In geometry we also find the midpoint. Now the question is What is the Midpoint Formula? as name implies, in the line segment the midpoint is the middle point. It is placed on the equal distance from both the endpoints that are starting point and end point or in other words we can say that it is method to find out the average of endpoints. That will become clearer when we will see the midpoint formula. Let’s discuss what the midpoint formula is. Midpoint formula is used to find out the midpoint from the line segment. So the midpoint formula for finding the midpoint of two points ‘x1’ and ‘x2’ that are on a line will be: - (x1 + x2) / 2. And the midpoint formula for finding the midpoint of a line segment with the endpoints (x1, y1) and (x2, y2) will be: -
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(x1 + x2) / 2, (y1 + y2) / 2, In above formula ‘x1’ indicates the first point x- coordinate and ‘x2’ indicates the second point y- coordinate and we are dividing it by 2 as same we are doing in y-coordinates. So now it is clear that it is like taking the average of endpoints. A midpoint separates the line segment into two equal two parts. So we have to follow the above formula whenever we will find the midpoint. Now let’s take a close look on midpoint to understand the midpoint formula more. Generally there are two methods to find out the midpoints on a line segment. First one is when our line segments are horizontal or vertical: In this type of situation we can easily find the midpoint by dividing the line segment by 2 and then count the value from both the endpoints. Such as we have PQ a vertical line segment that's value is 6 (value start from 0 to 5 means total 6) so the midpoint is 3 and MN a horizontal line segment that's value is 4, so the midpoint is 2. Although it can be more understand by graphically. -Second one is when our line segments are diagonally placed. In this situation we use following formula (x1 + x2) / 2, (y1 + y2) / 2. -Determine the midpoint value for the given value (-4, 6) and (8, -12). Solution: Here ‘x1’ and ‘x2’ and ‘y1’ and ‘y2’ are divided by the 2 values.
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Midpoint formula = (x1 + x2) / 2, (y1 + y2) / 2, -4 + 8 / 2, 6 â€“ 12 / 2, 2, -3, So the answer is 2, 3. Note: - It is to be noted that the midpoint formula works for both the cases. So the main aim of the midpoint formula is to determine the exact value between the endpoints. Sometimes it is assumed as the tool that is used to find out the midpoint of a line segment.
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