Coordinate geometry in the (x,y) plane

Question 1

Given two points (x₁,y₁) and (x₂,y₂), how can the midpoint of the two points be calculated?

Answer 1

((x₁+x₂)/2,(y₁+y₂)/2)

Question 2

What can be said about a line that passes through a circle’s centre that is perpendicular to a chord?

Answer 2

It bisects the chord

Question 3

Given two points (x₁,y₁) and (x₂,y₂), how can the distance between the two points be calculated?

Answer 3

√((x₂-x₁)²+(y₂-y₁)²)

Question 4

For three points A, B and C on a circle, with the line AC being a diameter, what can be said about the angle ∠ABC?

Answer 4

It is a right angle

Question 5

What is the equation of a circle with radius r and centre (a,b)?

Answer 5

(x-a)²+(y-b)²=r²

Question 6

What can be said about the angle between a radius and the tangent at the endpoint of the radius?

Answer 6

It is a right angle

Question 7

What is a chord?

Answer 7

A line that joins two points on the circumference of a circle

Question 8

What is a tangent?

Answer 8

A line that meets a circle at one point only