100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Summary Analytical Geometry - Mathematics Grade 12 (IEB) R50,00   Add to cart
Quickly navigate to
Preview
  2.  
  3. 12
  4.  
  5. Mathematics

Summary

Summary Analytical Geometry - Mathematics Grade 12 (IEB)

1 review
 159 views  0 purchase
  • Institution
  • 12

Covers the various sections relating to Analytical Geometry within the Mathematics syllabus. (Paper 2 section) Includes notes from the textbook, as well as additional...

[Show more]

Preview 2 out of 13  pages

Document information

  • February 23, 2021
  • 13
  • 2020/2021
  • Summary

Subjects

Written for

All documents for this subject (206)

1  review

review-writer-avatar

By: gerritcleroux • 3 year ago

Spelling

Seller

avatar-seller
KirstenBarbour

Reviews received

Content preview

Analytical geometry
Distance
For a vertical line: Ytop – Ybottom
For a horizontal line: Xright – Xleft

The distance formula: d = √(𝑥1 − 𝑥2 )2 + (𝑦1 − 𝑦2 )2
. or d2 = (𝑥1 − 𝑥2 )2 + (𝑦1 − 𝑦2 )2
Midpoints
𝑥1+𝑥2
For an x point: 2
𝑦1+𝑦2
For a y point: 2
𝑥1+𝑥2 𝑦1+𝑦2
The midpoint formula: (xm;ym) = ( ; )
2 2

Vertex to midpoint (medians)




Vertex dropped perpendicular to base (altitude)




Line dropped perpendicular to midpoint (perpendicular bisector)

, The gradient of a line
𝑟𝑖𝑠𝑒 ∆𝑦
M = 𝑟𝑢𝑛 = ∆𝑥
𝑦2−𝑦1
M=
𝑥2−𝑥1

Parallel lines: m1 = m2
Perpendicular lines: m1 x m2 = -1
Points are collinear if the gradient between any two = the gradient between any other 2

Positive gradient

- Makes acute angle with the x-axis
- Function is increasing
- Equation: y = mx + c

Negative gradient

- Makes obtuse angle with the x-axis
- Function is decreasing
- Equation: y = mx + c

Zero gradient

- Parallel to the x-axis
- Constant function
- Equation: y = c

Undefined gradient

- Perpendicular to the x-axis
- Vertical function
- Equation: x = b



The equation of a straight line
Y = mx + c (liner and first degree)

Finding the equation:
1. Get m
2. Substitute into y – y1 = m(x-x1)
3. Simplify

Finding m
∆𝑦
1. Graph ( m = ∆𝑥 )
2. Equation (y = mx+c)
𝑦2−𝑦1
3. 2 points (m = 𝑥2−𝑥1 )
4. Parallel lines (m1 = m2)
5. Perpendicular lines (m1 x m2 = -1)
6. Given angle (m = tan Ɵ)

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying this summary from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller KirstenBarbour. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy this summary for R50,00. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

83662 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy summaries for 14 years now

Start selling
R50,00
  • (1)
  Buy now