1. Find the length of the lines joining the following pairs of points (give answers correct to 3 significant figures):

a. (3, 4) and (6, 8)

b. (-3, 1) and (5, 6)

c. (4, 2) and (-5, 5)

d. (3, 6) and (-5, -2)

e. (-6, 2) and (3, -2)

f. (4, 5) and (2, -6)

2. Find the mid-point of the lines joining the following pairs of points:

a. (2, 5) and (8, 9)

b. (-2, -1) and (8, 4)

c. (5, -2) and (-6, 7)

d. (4, 1) and (-6, 3)

e. (-2, 4) and (6, -1)

f. (3, -5) and (1, -2)

3. Find the gradients of the lines joining the following pairs of points:

a. (-3, 4) and (3, -8)

b. (-1, 2) and (6, 9)

c. (3, -2) and (-4, 8)

d. (5, -2) and (4, -1)

e. (-5, 10) and (-3, -4)

f. (4, -5) and (3, -7)

For each of the following questions you may use a sketch to assist your reasoning but will be expected to use formulae and to show working to support your answers.

4. By finding the length of the three sides of the triangle, show that the triangle formed by joining the three points (7, 8), (2, 7) and (6, 3) is an isosceles triangle.

5. Show that the three points A(7, 5), B(1, 1) and C(-8, -5) lie on the same straight line.

6. Prove that the line passing through the points (-2, 4) and (6, 6) is parallel to the line joining the points (1, -2) and (-3, -3)

7. The three points (-2, 2), (6, 2) and (2, 5) form a triangle. Show that the triangle is an isosceles triangle.

8. Find the value of x so that the gradient of the line joining the points (x, 2) and (5, 10) is 2

9. Find the value of y so that the gradient of the line joining the points (2, y) and (-4, 2) is 0.5

10. The points (4,1), (7, -2), (1, -2) and (4, -5) lie on a circle. Find the coordinates of the centre of the circle.