50 441
Assignments Done
97,4%
Successfully Done
In July 2017
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.
Get a free quote.
Check the website
for updates.
Receive your completed assignment.
Easy as ABC!
Just provide us with clear instructions and wait for the completed assignment.

The Midpoint Theorem and Formula

Once a while in mathematics, we really need to find the midpoint between two other points, that is, the point that is exactly in the middle of the two other points. A good example is if you have to find the point at which a line bisects or divides a given line segment into two equal parts. The midpoint formula is quite simple and you should endeavour to know how to derive it for future use.

The midpoint formula can be conceived in terms of finding the middle number that exists between two given numbers such as 10 and 15. By adding the two numbers and dividing by 2, we obtain the exact middle number as follows:

Form1

Exactly the same way, the midpoint formula works. Let us consider the following question:

Find the midpoint between the points (-2, 4) and (6,-12).

Solution:

If we apply the midpoint formula, we have the following:

Form2

Hence, the coordinates of the midpoint = (2,-4)

The Midpoint Formula:

The midpoint formula is, therefore, given as:

Form3

This formula can be applied for solving different questions such as the followings:

1. If a line segment has its endpoints given as (-1.8, 3.9) and (8.2,-1.1), determine whether the equation y=2x-4.9 is a bisector of this line segment.

Solution:

The exact midpoint of the line segment can only be determined by applying the midpoint formula and not by graphical method. Hence, by applying the midpoint formula, we have:

Form4

Now, check to see if this point is on the line y=2x-4.9.

y=2x-4.9

y=2(3.2)-4.9=6.4-4.9=1.5. But, y, ought to be equal to 1.4 as the y-coordinate of the midpoint indicates. Therefore, y=2x-4.9 is not a bisector of the line segment.

2. Find the bisector of the line segment given above.

To find the perpendicular bisector of this line segment, you will need to solve the problem in a multi-parts manner. Note that this is one of the typical questions you will surely come across as you proceed in your learning of maths particularly the straight lines. The procedure for solving this problem is simple and straight forward and it is given as follows:

First of all, determine the midpoint of the line segment by applying the midpoint formula given above.

Form5

The slope of the line segment is needed here; therefore, we obtain the slope as follows:

Slope,

Form6

this is a negative reciprocal which must be flipped.

So, the slope, m=2 (since negative reciprocal means that it should be changed).

The equation of the bisector of the line segment is therefore obtained as follows:

y – y1 = slope(x – x1)

y – 1.4 = 2(x – 3.2)

y = 2x – 5.

Comments are closed.