Thursday, March 21, 2013

Transformations Geometry

Introduction for transformations geometry:

The transformation Geometry is a copy of a geometric figure, where the copy holds some certain property. The original shape is called the pre-image the new picture is called the image of the transformation. A transformation is single in which the pre-image and the figure equally has the exact same dimension and shape. I like to share this Definition of Parabola with you all through my article.


Basic Transformation Geometry:


The two types of transformation geometry is given by

Rigid transformations

Non-rigid transformations.

This page will covenant with three rigid transformations known as translations, reflections and rotations.

About geometry transformations:

The main geometry transformations in the mathematics are given as,

Translations

Reflections

Rotations

Scaling

Shear

Translations:

The mainly basic transformation is the translation. The definition of a translation is the pre-image and then it can be moved to the equal distance in the same direction to form the image .The transformation is would be

T(x, y) = (x+7, y+4).

Reflections:

The reflection is a "flip" of an aim over a line.

The two very common reflections is given by

horizontal reflection

vertical reflection.

The line of reflection will be both red points, blue points, and green points. The line of reflection which is directly in the center of both points. Having problem with Surface Area of a Circle keep reading my upcoming posts, i will try to help you.


Other types of Transformations:


Rotations:

The transformations which are performed by spinning the object just about a point of the center rotation .You can able to change your object at some of the degree measure, but 90° and 180° are very important degrees.

Rotation 180° around the origin: T(x, y) = (-x, -y)

Scaling:

The scaling is a linear transformation which diminishes the objects and the scale factor is same for direction is called scaling. The resultant image of the uniform scaling is similar to the original transformations

Shear:

The Shear which transforms effectively to rotate one axis and that the axes are no longer at right angle. A rectangle becomes a parallelogram, and a round becomes an ellipse. Constant lines parallel to the axes continue the same length, others do not. As a plot of the plane, it deception in the class of equilateral mappings.

Tuesday, March 19, 2013

Geometry Definitions

That branch of mathematics which investigates the relationship, properties, and measurement of solids, surfaces, lines, and angles; the science which treats of the properties and relations of magnitudes; the science of the relations of space.


Line


In geometry a line:

·         is straight (no curves),

·          has no thickness, and

·         extends in both directions without end (infinitely)


Line segment:


If it does have ends it would be called a "Line Segment".

"Line" normally means straight, so say "curve" if it has a curve.

The word "segment" is significant, because a line normally extends in both directions without end.


angle-angle-angle (AAA) similarity


The amount of turn between two straight lines that have a common end point (the vertex). An acute triangle is a triangle with all angles lesser than 90 degrees.

The angle-angle-angle (AAA) relationship test says that if two triangles have corresponding angles that are congruent, then the triangles are similar. Because the sum of the angles in a triangle must be 180°, we really only need to know that two pairs of corresponding angles are congruent to know the triangles are similar.

The centroid of a triangle is the point where the three medians meet. This point is the center of mass for the triangle. If you cut a triangle out of a piece of paper and put your pencil point at the centroid, you could balance the triangle.Having problem with Surface Area Sphere keep reading my upcoming posts, i will try to help you.


Congruent


Two figures are congruent if all corresponding lengths are the equal, and if all corresponding angles have the same measure. Colloquially, we say they "are the same size and shape," though they may have different orientation. (One might be rotated or flipped compared to the other.)

Sat Geometry Problems

Introduction of sat geometry:
The Abbreviation of SAT is Scholastic Aptitude Test. This test is used for admission to college in United States. The total time has given for SAT test is 70 minutes.There are two sections , one section is given 50 minutes, another section is given 20 minutes.

Topics of sat geometry:

Area and perimeter of a polygon in sat geometry

Area and circumference of a circle in sat geometry

Volume of a box, cube and cylinder in sat geometry

Pythagorean Theorem in sat geometry

Coordinate geometry in sat geometry

Slope

Triangles


SAT Geometry Problems


Problem1:

Which one of these have the largest volume?

Square based prism with sides 7

Rectangular prism of dimensions 5x5x4

Rectangular prism of dimensions 5x6x8

Cylinder of base radius 3 and height 6

Cylinder of base radius 3 and height 8

Problem 2:

My triangular prism has a triangle base with base 5 and height 6, and the prism has a height of 7. What is the volume of the triangular prism?

96

24

100

84

105

Problem 3:

My shape has 4 sides. One of which are parallel. The sides are not all equatl. What shape do I have?

Parallelogram

Trapezoids

Rhombus

Prism

Problem 4:

I have a polygon with 6 equal sides that has 6 equal angles. What is the size of each angle?

180

120

90

154.3

720

Problem 5:

What is the equation of a line with slope is -2 and y intercept is -1 is ?

2x-y+2=0

2x+y+1=0

2x+y-1=0

Is this topic Area of Ellipse hard for you? Watch out for my coming posts.

Problem 6:


The slope of the line 3x+4y+5 = 0 is

3/4

4/3

-3/4

Problem 7:

The straight line x+2y+7=0 passes through (3,k) then valuee of k=?

5

-5

0

Problem 8:

Equation of line parallel to y-axis and passing through the point (3,2) is ?

X = 3

x = -3

y = -3

Problem 9:

A line passing through (0,3) and (4,5) is ?

x – 2y +6 = 0

2x – y + 6 = 0

x – 2y - 6 = 0

Problem 10:

What is the perimeter of my triangle with given three vertices (2,3), (6,2) and (4,2)?

9.7

9.0

8.9

7.9