Co-ordinate Geometry 2 25 th November 2019 Welcome! Coordinate - - PowerPoint PPT Presentation

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Co-ordinate Geometry 2 25 th November 2019 Welcome! Coordinate - - PowerPoint PPT Presentation

Jan 26, 2023 344 likes •471 views

Co-ordinate Geometry 2 25 th November 2019 Welcome! Coordinate Geometry 1. The Line Key Concepts Revision 2. Circle Question Focused Approach 1.5 hours - 10mins break @7pm Any questions? Just Ask!! Useful Resource for

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SLIDE 1

Co-ordinate Geometry 2

25th November 2019

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SLIDE 2
  • Coordinate Geometry –
  • 1. The Line – Key Concepts Revision
  • 2. Circle
  • Question Focused Approach
  • 1.5 hours - 10mins break @7pm
  • Any questions? – Just Ask!!

Welcome!

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SLIDE 3
  • www.themathstutor.ie
  • Normally €99.99
  • Discount code: SAI
  • €49.50 for the year
  • Access only to June 2019

Useful Resource for Project Maths

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SLIDE 4
  • Slides, questions and solutions available

from website: https://web.actuaries.ie/students/tutorials

  • Or google ‘actuaries maths tutorials’ to find

it. Material from tonight

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SLIDE 5
  • Read the question carefully.
  • Key formula tables – page 18 & 19.
  • Know your theorems.
  • Draw a diagram every time.
  • Label all diagrams.
  • Write down your workings.
  • Is your result plausible?

Exam Technique:

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SLIDE 6

A(x1,y1) and B(x2,y2) are points on a line k. The slope m = (y2-y1)/(x2-x1) Given two points A(x1,y1) and B(x2,y2),

  • r given one point A(x1,y1) and the slope m,

equation of line:

(𝑧−𝑧1) (𝑦−𝑦1) = (𝑧2−𝑧1) (𝑦2−𝑦1) [= m]

  • r

(𝑧−𝑧1) (𝑦−𝑦1) = m

Line

y x O A(x1,y1) B(x2,y2) k y2-y1 x2-x1

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SLIDE 7

y y = mx + c c O x The equation of the line can be written in the form: y = mx + c (c the intercept on the y-axis, where x=0) m can be positive (concave angle with x-axis)

  • r negative (convex angle with x-axis).

Lines with same slope are parallel. Lines with slopes m and -1/m are perpendicular. The equation of the line can also be written in the form ax+by+c = 0 (for use in formulae)

Line

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SLIDE 8

Circle

(x-h)2 + (y-k)2 = r2 r (h,k) x-h (x,y) y-k Centre (h,k) Radius r

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SLIDE 9
  • Key formulae – page 19

Circle

Find inding th the e eq equation of

  • f a

a ci circle: (𝑦 − ℎ)2+(𝑧 − 𝑙)2= 𝑠2 Formula for circle with centre (h, k) 𝑦² + 𝑧² = 𝑠² Formula for circle with centre (0, 0) Find inding th the e cen centre an and rad adius of

  • f a

a ci circle: Express the circle in this form: 𝑦2 + 𝑧2 + 2𝑕𝑦 + 2𝑔𝑧 + 𝑑 = 0 Centre of the circle is (-g, -f) Radius of the circle is √(g2 + f2 – c)

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SLIDE 10

Circle

The The pe perpe pendicular bi bisector of

  • f an

any ch chord is is a a lin line co containing th the cen centre of

  • f th

the ci circle

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SLIDE 11
  • Monday 2nd December
  • Trigonometry 2
  • Same location
  • 6 - 8 pm
  • https://web.actuaries.ie/students/tutorials

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