Euclidean geometry is the study of shapes, sizes, and positions based on the principles and assumptions stated by Greek Mathematician Euclid of Alexandria. It is also called the geometry of flat surfaces. Euclidean geometry is limited to the study of straight lines and objects usually in a 2d space. In practice, Euclidean geometry cannot be applied to curved spaces and curved lines.
Euclid’s geometrical mathematics works under set postulates (called axioms). Euclid’s axioms were considered the base of mathematics related to geometry for almost 2000 years until Einstein’s theory of relativity offset his theories and proved his postulates wrong in relative dimensions of geometry.
The entire bulk of Euclidean geometry is based on 5 axioms or assumptions:
A straight line joins two points
A straight line can be elongated on both sides to infinity
A circle can be made if a point is given as the center and a measure is given for its radius
All right angles are equal
If a straight line intersects two lines the interior angles on the same sides will always have a sum less than 90∘.
Any system that violates the said axioms comprises non-Euclidean geometry.
To calculate the midpoint of a line in the coordinate sysytem we do
x AB= Xb+Xa/2 y AB= Ya+ Yb/2
xAB=7/2 y AB= 5
This answer is incorrect, there is no way that you can get -8b. The correct answer is 11a+2b
It can be tricky to calculate the cosine of an angle, however, some ways can make the process easier. The easiest way to calculate the cosine of an angle is to find the length of an adjacent side and divide it by the hypotenuse. The technical terms themselves can trip people up sometimes more than the calculating itself.
Adjacent means that a line is next to or connecting to another line. The hypotenuse is the longest side of a right angle. When all of these terms and processes are understood finding the cosine of an angle becomes an easy thing to do.
Arithmetic is the most elementary division of mathematics. It involves the simple manipulation of numbers, which refers to adding, subtracting, multiplying, and dividing. Geometry, on the other hand, points to the branch of mathematics that describes the properties of bodies in space, which refers to lines, planes, points, angles, and figures. Arithmetic and geometry help man quantitatively explain his world. Arithmetic is the foundation of all other math, and it is used extensively in our lives; however, geometry is widely used in construction. Geometry governs principles behind figures and lines, while basic math is used in our everyday lives.
The figure is Translated right by 4 and
Translated up by 2