1. BASIC Point Formulas Distance, Midpoint, Gradient By Mr Porter
Coordinate Geometry I x1 x2 y2 y1
P(x1,y1)
Q(x2,y2)
Y-axis
X-axis
YOU NEED TO KOWN THE FORMULAE !
BASIC Point Formulas
Distance, Midpoint, Gradient
By Mr Porter

2. YOU NEED TO KOWN THE FORMULA !
Distance between 2 Points P(x1, y1) and Q(x2, y2)
(x1, y1)
(x2, y2)
Example 1: Find the distance between A(1,-3) and B(5,7).
Helpful Hints:
It is usually a good idea to make a little sketch.
Write down ALL point formulae used in coordinate geometry.
Label points clearly (x1, y1) & (x2,y2)
Is your answer what you expect or realistic for the problem.
1) Formula :
YOU NEED TO KOWN THE FORMULA !
2) Show substitution into formula clearly.
Use calculator to evaluate (5-1)2 + (7--3)2
A(1,-3)
B(5,7) 4 10
Simplify the surd.
The exact distance between A(1, -3) and B(5, 7) is

3. YOU NEED TO KOWN THE FORMULA !
(x1, y1)
(x2, y2)
Example 2: Find the distance between P(-3,5) and Q(5,-5).
Helpful Hints:
It is usually a good idea to make a little sketch.
Write down ALL point formulae used in coordinate geometry.
Label points clearly (x1, y1) & (x2,y2)
Is your answer what you expect or realistic for the problem.
1) Formula :
2) Show substitution into formula clearly.
YOU NEED TO KOWN THE FORMULA !
P(-3, 5)
Q(5,-5) 10 8
Use calculator to evaluate (5--3)2 + (-5-5)2
Simplify the surd.
The exact distance between P(-3, 5) and B(5, -5) is

4. YOU NEED TO KOWN THE FORMULA !
Mid-Point of 2 Points P(x1, y1) and Q(x2, y2)
(x1, y1)
(x2, y2)
Example 1: Find the Mid-Point of A(1,-3) and B(5,7).
Helpful Hints:
It is usually a good idea to make a little sketch.
Write down ALL point formulae used in coordinate geometry.
Label points clearly (x1, y1) & (x2,y2)
Is your answer what you expect or realistic for the problem.
1) Formula: (average point / co-ordinates)
YOU NEED TO KOWN THE FORMULA !
2) Show substitution into formula clearly.
A(1,-3)
B(5,7) 4 10
The mid-point of A(1, -3) and B(5, 7) is (3, 2).

5. YOU NEED TO KOWN THE FORMULA !
(x1, y1)
(x2, y2)
Example 2: Find the mid-point of P(-3,5) and Q(5,-5).
Helpful Hints:
It is usually a good idea to make a little sketch.
Write down ALL point formulae used in coordinate geometry.
Label points clearly (x1, y1) & (x2,y2)
Is your answer what you expect or realistic for the problem.
1) Formula :
YOU NEED TO KOWN THE FORMULA !
2) Show substitution into formula clearly.
P(-3, 5)
Q(5,-5) 10 8
The mid-point of P(-3,5) and Q(5,-5) is (1, 0).

6. YOU NEED TO KOWN THE FORMULA !
Gradient, m, of line joining 2 Points P(x1, y1) and Q(x2, y2)
(x1, y1)
(x2, y2)
Example 1: Find the gradient, m, of the line passing through points A(1,-3) and B(5,7).
Helpful Hints:
It is usually a good idea to make a little sketch.
Write down ALL point formulae used in coordinate geometry.
Label points clearly (x1, y1) & (x2,y2)
Is your answer what you expect or realistic for the problem.
1) Formula :
YOU NEED TO KOWN THE FORMULA !
2) Show substitution into formula clearly.
A(1,-3)
B(5,7) 4 10 
Always try to write the gradient, m, as a simplified IMPROPER fraction
The gradient of the line passing through A(1,-3) and B(5,7) is :

7. YOU NEED TO KOWN THE FORMULA !
(x1, y1)
(x2, y2)
Example 2: Find the gradient, m, of the line passing through points P(-3,5) and Q(5,-5).
Helpful Hints:
It is usually a good idea to make a little sketch.
Write down ALL point formulae used in coordinate geometry.
Label points clearly (x1, y1) & (x2,y2)
Is your answer what you expect or realistic for the problem.
1) Formula :
YOU NEED TO KOWN THE FORMULA !
2) Show substitution into formula clearly.
P(-3, 5)
Q(5,-5) 10 8 
Always try to write the gradient, m, as a simplified IMPROPER fraction
The gradient of the line passing through P(-3,5) and Q(5,-5) is :

8. YOU NEED TO KOWN THE FORMULAE !
Exercise
1) Given the two points A(-3,7) and B(5,1) find the
a) distance AB
b) point C, the mid-point of interval AB
c) gradient, mAB, of the line joining AB
(x1, y1)
(x2, y2)
Helpful Hints:
It is usually a good idea to make a little sketch.
Write down ALL point formulae used in coordinate geometry.
Label points clearly (x1, y1) & (x2,y2)
Is your answer what you expect or realistic for the problem.
Simplify all surds!
The distance AB is d =
The gradient of line AB is
A(-3,7)
B(5,1)
The mid-point C is (1,4)
YOU NEED TO KOWN THE FORMULAE !

9. YOU NEED TO KOWN THE FORMULAE !
Exercise
2) Given the two points P(-5,-3) and Q(6,4) find the
a) distance PQ
b) point R, the mid-point of interval PQ
c) gradient, mPQ, of the line joining PQ
(x1, y1)
(x2, y2)
Helpful Hints:
It is usually a good idea to make a little sketch.
Write down ALL point formulae used in coordinate geometry.
Label points clearly (x1, y1) & (x2,y2)
Is your answer what you expect or realistic for the problem.
The distance PQ is d =
The gradient of line PQ is
P(-5,-3)
Q(6,4)
The mid-point R is
YOU NEED TO KOWN THE FORMULAE !

10. YOU NEED TO KOWN THE FORMULAE !
Exercise
3) Given the two points L(8,-3) and M(-1,5) find the
a) distance LM
b) point K, the mid-point of interval LM
c) gradient, mLM, of the line joining LM
(x1, y1)
(x2, y2)
Helpful Hints:
It is usually a good idea to make a little sketch.
Write down ALL point formulae used in coordinate geometry.
Label points clearly (x1, y1) & (x2,y2)
Is your answer what you expect or realistic for the problem.
The distance LM is d =
The gradient of line LM is
M(-1,5)
L(8,-3)
The mid-point K is
YOU NEED TO KOWN THE FORMULAE !

11. YOU NEED TO KOWN THE FORMULAE !
FORMULAE TEST
Given the two points P(x1,y1) and Q(x2,y2)., write down the formula for:
a) Distance PQ
b) Mid-point of the interval PQ
c) Gradient of the interval PQ.
YOU NEED TO KOWN THE FORMULAE !
These will be revised again in HSC application type questions.