Introduction
Welcome Grade 10 learners
SUBJECT: MATHEMATICS
LESSON TOPIC: ANALYTICAL GEOMETRY
Introduction: check the following link
Task
1. Determine the length of AB, if these coordinates are given A(2;1) and B (6;-4)
2. A(-2;4), B(K;-8), C(-5;1) are given with AB=BC
2.1) Determine the value of K.
2.2) What type of triangle is ABC
3. Consider the points J(-4;1), K(-1;-3), L(3;0), M(0;-4)
3.1) Show that JKLM is a rhombus
3.2) is JKLM a square justify your answer
4. Calculate the gradient of PQ and QR if P(2;3), Q(-4;-1), R(6;-3)
5. Points M(-3;2), N(6;-8), P(12;10), R(-2;7)
5.1) show that RN=MP
5.2) is RM||PN? justify your answer
6. If P(-7;-1) and Q (3;2) are given determine the midpoint of PQ
Process
INSTRUCTIONS:
- The task consists of 6 questions.
- Answer all the questions
- Number the questions correctly according to the numbering system used in this task.
- Show all your workings
- Use a scientific calculator
- Note show the formula you using
- Leave a line after each answer
- Write neatly and legibly.
Evaluation
Understanding the problem correct use of formula
Complete understanding of problem using correct formula 2
Partially of the problem was misinterpreted 1
complete misunderstanding of the problem 0
Planing a solution
Implemented correctly all steps are correct 2
Partially correct plan based on part of the problem being interpreted correctly 1
no attempt 0
Getting a solution or solving the problem
Correct answer and correct label for answer all steps of the problem are correct 2
Did not result in a solution that solved problem 1
Wrong answer based on inappropriate plan 0
Conclusion
Learners should always write down the formula before attempting to question as this will help them to remember the formulas and to use them correctly. The learners must be able to use and apply formulas to calculate the distance, gradient, and midpoint of geometric figures on the Cartesian plane.
Geometry formulas
Distance is a measure of the length between two points. The formula for finding the distance between any two points is:
The gradient between two points is determined by the ratio of vertical change to horizontal change.
If two lines are parallel, their gradients are equal
If two lines are perpendicular the products of their gradients are equal to -1
For horizontal lines, the gradient is equal to zero
For vertical lines, the gradient is undefines
The midpoint formula is used for finding the mid-point between two points
Credits
sources: Grade 10 MATHEMATICS PLATINUM
Teacher Page
Miss Lisa Ngomane
email: ngomanelisa00@gmail.com