Coordinate geometry

Question 1

Formula to calculate gradient

Answer 1

gradient = change in y / change in x

Question 2

Formula to calculate midpoint

Answer 2

midpoint = ( x1 + x2 /2 , y1 + y2 / 2)

Question 3

Formula to calculate length

Answer 3

length = √(x2 - x1)^2 + (y2 - y1)^2

Question 4

Equation of a straight line and its alternative form

Answer 4

y = mx + c
- c represents the y intercept
- m represents the gradient
alternative form:
y - y1 = m(x-x1)

Question 5

Describe parallel and perpendicular lines

Answer 5

• If two lines are parallel, they have the same gradient
• If two lines with gradients m1 and m2 are perpendicular, then m1 x m2 = -1

Question 6

Describe how to find the intersection of 2 lines

Answer 6

• point of intersection can be found by solving the equations of the line simultaneously
• if both equations are given in the same form, you can make them equal to each other and solve
• you could also use the elimination method

Question 7

General equation of a circle, centre the origin and radius r

Answer 7

x^2 + y^2 = r^2

Question 8

General equation of a circle, centre (a, b) and radius r

Answer 8

(x-a)^2 + (y-b)^2 = r^2

Question 9

3 facts about the properties of a circle

Answer 9

1. the angle in a semi-circle is a right angled triangle
2. the perpendicular from the centre of a circle to a chord bisects (cuts in half) the chord
3. the tangent to a circle is perpendicular to the radius at that point