C2 Coordinate Geometry

Question 1

How do find the mid-point of the line joining (x1,y1) and (x2,y2)?

Answer 1

mid-point = ((x1 + x2)/2,(y1 + y2)/2)

Question 2

How do find the gradient of the line joining (x1,y1) and (x2,y2)?

Answer 2

m = (y2 - y1)/(x2 - x1)

Question 3

How do find the length of the line joining (x1,y1) and (x2,y2)?

Answer 3

l = ((x2 - x1)^2+(y2-y1)^2)^1/2

Question 4

What is the general formula for a circle?

Answer 4

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

with radius r and centre (a,b)

Question 5

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

What is this a formula for?

Answer 5

A circle with radius r and centre (a,b)

Question 6

What if the equation for a circle with radius 7 and centre (-4,8)

Answer 6

(x + 4)^2 + (y - 8)^2 = 49

Question 7

How can you show that two lines are parallel?

Answer 7

By showing that their gradients are the same.

Question 8

How can you show that two lines are perpendicular?

Answer 8

By showing that the product of their gradients is -1.

Question 9

What is a chord?

Answer 9

A line joining two points on an circumference.

Question 10

What is the angle between a chord and the line joining its mid-point and the circle’s centre?

Answer 10

90°

Question 11

What is the angle on the circumference subtended by the diameter?

Answer 11

90°

Question 12

What is the angle between a radius and a tangent?

Answer 12

90°

Question 13

At how many points do a circumference and its tangent meet?

Answer 13

Once.