Chapter 5 Coordinate Geometry

Question 1

What is the formula for the distance AB?

Answer 1

This represents the calculation of distance between points A and B.

Question 2

Which theorem is used to calculate distance?

Answer 2

Pythagoras’ Theorem

Question 3

How do you find the midpoint?

Answer 3

This indicates the calculation for finding the midpoint between two points.

Question 4

How do you calculate the gradient of a line segment?

Answer 4

This shows the relationship between the gradient and the coordinates of points A and B.

Question 5

What are the coordinates for line segment A and B?

Answer 5

For a line segment A (x1,y1) and B(x2, y2)

This defines the coordinates used in the context of the line segment.

Question 6

What does it mean for two lines to be parallel?

Answer 6

Two lines are parallel if their gradients are equal.

Question 7

What does it mean for two lines to be perpendicular?

Answer 7

Two lines are perpendicular if the product of their gradients is -1.

m1 x m2 = -1

Question 8

What is the equation of a line parallel to the y-axis?

Answer 8

The equation of a line parallel to the y-axis is x = a.

Question 9

What is the equation of a line parallel to the x-axis?

Answer 9

The equation of a line parallel to the x-axis is y = b.

Question 10

What is the equation of a line through the origin with gradient m?

Answer 10

The equation is y = mx.

Question 11

What is the equation of a line through (0, d) with gradient m?

Answer 11

The equation is y = mx + d.

Question 12

What is the equation of a line through (x₁, y₁) with gradient m?

Answer 12

The equation is y - y₁ = m(x - x₁).

Question 13

What is the equation of a circle with centre (0, 0) and radius r?

Answer 13

The equation is x² + y² = r².

Question 14

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

Answer 14

The equation is (x - a)² + (y - b)² = r².

Question 15

What is the angle in a semicircle?

Answer 15

The angle in a semicircle is a right angle.

Question 16

What does the perpendicular from the centre of a circle to a chord do?

Answer 16

It bisects the chord.

Question 17

What is the relationship between the tangent to a circle and the radius at that point?

Answer 17

The tangent to a circle at a point is perpendicular to the radius through that point.

Question 18

How do you find the points of intersection of two curves?

Answer 18

You solve their equations simultaneously.