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Coordinate Geometry of The Line - Maths
32 students
What you'll learn
- The course covers the concepts, theory and practice questions required to understand and use coordinate geometry to solve mathematical problems.
- The course will provide the ability to solve geometric problems using algebraic methods
- You will have the opportunity to evaluate and support your new knowledge through fully worked and explained exam questions.
- Students of the Leaving Certificate maths exam will have plenty of opportunity to practice at exam level with 10+ years of exams questions included.
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Course content
13 sections • 15 lectures • 2h 47m total length
Requirements
- Ability to preform basic algebraic operations (+-×÷) is desirable.
- Scientific Calculator eg Casio fx-85GT
Description
Learn how to solve geometric problems using algebraic methods. This course covers the concepts, formulae and methods required for Coordinate Geometry, an area of maths developed by Rene Descartes. The course structure is based on the Leaving Certificate maths syllabus.
The course content is broken into the following eleven modules:
Distance between two points:
Learn how to find the distance between two given points or the length of a line segment using the distance formula or Pythagoras Theorem Equation.
Midpoint of a line segment:
Learn how find the midpoint of a line segment using the midpoint formula or by using the geometric transformation of translations.
Slope of a line:
Learn how to find the slope of a line depending on what information is available. Find slope using the two points formula. Use the formula rise over run if given the graph with the line plotted. Find the slope directly from the equation using using the coefficients of the x and y terms. Find the slopes of parallel and perpendicular lines.
Equation of a line:
Learn how to find the equation of a line using the formula for a point and slope. Use the formula y=mx+c if given the line plotted. Find the equation of parallel and perpendicular lines.
Graphing lines on a coordinate diagram:
Learn how to plot and graph lines using input/output table, from the equation of the line and using a calculator. Learn the properties of linear functions, domains and codomains.
Points of interest:
Learn how to find particular points like point of intersection of two lines, x and y intercept on the axis and also testing if a point is on a line. Learn how to solve simultaneous equations using the method of elimination.
Area of a triangle:
Learn how to find the area of a triangle using the area formula or the geometry formula of half the base by the perpendicular height. Learn how to perform translations before using the formula. Find the area of quadrilaterals and regular polygons.
Internal Point Divisor of a Line:
Learn how to find the coordinates of an internal point divisor of a line segment using the formula or by translation. The ratio can be converted to quotients which can be used with the operation of a translation.
Angles between two lines:
Learn how to find the acute and obtuse angles at the point of intersection of two lines. Know that the formula finds the acute angles and learn how to then find the obtuse angle.
Perpendicular distance:
Learn how to find the shortest distance between two parallel lines by using the formula. The formula requires a point on one line and the equation of the other.
Centres of a triangle:
Learn how to find the coordinates of the centroid, circumcentre and orthocentre of a triangle using coordinate geometry. Learn particular properties of these centres which are useful for more in depth questions.
This course covers coordinate geometry which is also known as Cartesian Maths and analytical geometry.
Who this course is for:
- This course is suitable for Leaving Certificate students at Ordinary or Higher level maths. Past exams questions are fully worked and explained.
- This course is ideal for students aged 16-18 years old who are studying maths in school and would benefit from clear explanations and fully worked and explained questions.
- University students of many disciplines (eg science, engineering) will find this course of value as a revision of coordinate geometry.
- Home Schoolers, both parents and students, will find the progressive structure of the course gives the correct path for learning coordinate geometry.
- Anyone who wants to achieve knowledge of maths will find this course approachable and rewarding.
- Coordinate geometry is a required knowledge for coding, particularly gaming.