Looking for ways to deal with analytic geometry homework issues? Then read this article because here you can brush up your concepts related to analytical geometry and gain complete knowledge on how to solve analytical geometry homework problems in the lesser time limit and with more efficiency.
You already know what analytical geometry is, but there is no harm in reminding you the universal definition of analytical geometry. It is a branch of algebra that is used to model geometric objects, wherein points (straight), lines and circles are considered as the most basic elements.
Basic concept of analytical geometry
Learn the basic concepts of analytical geometry well because they are mandatory while doing a geometry homework assignment.
- The core concept of analytical geometry is based on the use of a coordinate system that relates geometric points to real numbers. This discipline allows you to define each point with a unique set of real numbers and geometric figures such as circles, lines and conics that can be described with algebraic equations.
- In analytical geometry, algebraic equations are graphically represented in any form – rational functions, graphs of polynomials, conic sections, exponential and logarithmic functions, hyperbolas and even vectors. The process is known as graphing.
- X-axis and Y-axis are where the x and y values are plotted along. Origin is symbolized by 0 and denotes the value of 0 of both axes. The coordinates are given in the form (x, y) and are used to represent different points on the plane.
- Inclination of a line: It is the smallest angle — ÆŸ, which is greater than or equal to 0° — that the line makes with the positive direction of the x-axis (0° ≤ ÆŸ < 180°).
- Slope of a line: It is the tangent of the inclination defined as m = tan ÆŸ, where m = the slope of the line and ÆŸ = inclination angle.
- Slope of a line: When passing through two given points P1 (x1, y1) and P2 (x2, y2), it is equal to the difference of the ordinates divided by the differences of the abscissas taken in the same order.
- Theorems of slope:
- Two non-vertical lines are parallel only if their slopes are equal.
- Two slant lines are perpendicular if the slopes of one are the negative reciprocal of the slope of the other.
- If ÆŸ is angle ( ÆŸ = standard position) measured anti-clockwise between two lines, then
m2= the slope of the terminal side
m1= the slope of the initial side
- The distance between two points in the plane is defined by the length of the line segment joining two points. If the points have cartesian coordinates, ( and (), the distance would be
The midpoint of two points, (x1,x2)and (y1,y2) would then be ,
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Concepts are foundation of any subject and analytical geometry is no different. If you want to excel in geometry homework, it is better to strengthen your foundation before jumping into the advanced level. Geometry homework assignments cannot be solved if you don’t hone the concepts of analytical geometry.
If you simply copy-paste geometry homework solution from electronic sources, you need to remember that mathematics is not about duplication, it is about resolving the given problem. When geometry homework assignments are given to the students, they face difficulty with the use of the formula at the appropriate place. Hence, they are unable to complete analytical geometry homework and worst they are unable to explain how they have arrived at the results when asked by the tutors. Geometry is all about difficulties so you have to follow the instructions and improve your knowledge level. On that matter, MyAssignmenthelp.com gives you a helping hand in solving geometry homework assignments.
Analytical geometry always follows sensible and accurate methods. While you are dealing with analytical geometry homework assignments, you need to follow a single formulae or method to obtain a result. But students get perplexed when they do not understand which formulas they have to implement in what situation. For that reason, logic and practice are two factors that allow students to have a grip over this discipline of study. On that very matter, MyAssignmenthelp.com provides a one-stop solution to all those who want to deal with geometry homework problems.
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Solving geometry homework assignments will be a lot easier if you take help with MyAssignmenthelp.com. For further geometry homework assignment help, we demonstrate few practical geometry homework assignment solutions.
Practical examples (Step-by-step tutorial)
To solve all the problems, you first need to remember this equation of slope:
Analytical geometry homework example 1: Find the slope of the line that passes through the points P1 (1,2) and P2 (3,4)
In this problem,
X1 = 1
Y1 = 2
X2 = 3
Y2 = 4
The equation would be,
Since ‘m’ here is +1, the slope inclines to the right.
Analytical geometry homework example 2: Find the slope of the line that passes through the points (-1, 3) and (2, 1)
Applying the slope formula,
As you can see the line has negative values, so it inclines to the left.
Analytical geometry homework example 3: Find the slope of the horizontal line y = 1.
In order to find the slope of the line, let P1 (x1, Y1) = (-2, 1) and P2 (X2, Y2) = (2,1) be the two points on the line, thus, we have:
The line is horizontal, so it has a zero slope.
Analytical geometry homework example 4: Find the slope of the vertical line x = - 2. Draw the line.
x= -2 is a vertical line that intersects the x-axis at -2.
So, let P1 (X1, Y1) = (-2, 1) and P2 (X2, Y2) = (-2, 3) be the two the points on the line.
The line is vertical, so its slope is undefined.
Analytical geometry homework example 5: Find the distance between the points (2, -3) and (-4, 4)
Here, we will use this formula,
Analytical geometry homework example 6: Identify the type of triangle formed by the points
A = (6, 0)
B = (3, 0)
C = (6, 3)
You can see two angles are same which means it is an isosceles triangle.
These are only few examples. If you avail our geometry homework help, we assure you that our tutors will make you understand the concepts better with their geometry homework tutorials. It will become a lot easier for you to perceive the concepts and implement them in your geometry homework writing.
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