WORKSHEET ON CO-ORDINATE GEOMETRY
1. On the grid below, plot the following points:
a) P (-3,-4)
b) Q (0,5)
c) R (8,-9)
d) S (-6,0)
2. Consider the points A (-2,0), B (2,1), C (1,-3).
Determine if triangle ABC is equilateral, isosceles or scalene.
3.
Use the Diagram above to find the co-ordinates of the mid-point of:
a) GA
b) CD
c) FB
4. AB is the diameter of a circle with centre C. If A is (3,-2) and B is (-1, -4). Find the co-ordinates of C.
5. The mid-point, M, of the line joining 𝐴(𝑠, 8) 𝑡𝑜 𝐵(−2, 𝑡) has co-ordinates 𝑀(2,3).
a) Calculate the values of 𝑠 and 𝑡.
b) Find the equation of the straight line perpendicular to AB, passing through the point M.
6. P (4,1) and Q (0,-5) are points on the co-ordinate plane.
a) Determine the
i)
Co-ordinates of M, the mid-point of P and Q.
ii)
Gradient of the line drawn through P and Q.
iii)
Gradient of the line drawn through M, perpendicular to PQ.
The perpendicular line drawn through M meets the y-axis at 𝑅 (0, 𝑘)
b) Find 𝑘.
7. Three points are given A (0,4), B (6,0) and C (8,3).
a) Calculate the gradient (slope) of line AB.
b) Find the co-ordinates of the midpoint, M, of the line AC.
c) Calculate the length of line AC
d) Find the equation of the line BM giving your answer in the form 𝑎𝑥 + 𝑏𝑦 + 𝑑 = 0,
where 𝑎, 𝑏 𝑎𝑛𝑑 𝑑 ∈ ℤ.
e) State whether the line AB is perpendicular to the line BC showing clearly your working and
reasoning.
8. Points 𝑃 (0. −4), 𝑄 (0,16) are shown on the grid:
a) Plot the point R (11,16)
b) Calculate angle QPR.
M is a point on the line PR. M is 9 units from P.
c) Calculate the area of triangle PQM.
9. A is the point (2,3) and B is the point (4,9).
a) Find the gradient of the line segment AB
b) Find the gradient of a line perpendicular to the line segment AB
c) The line 2𝑥 + 𝑏𝑦 − 12 = 0 is perpendicular to the line segment AB. What is the value of 𝑏?
10. Two points are given as A(4,3) and B(5,7).
a) Plot these points on the grid below.
b) Join the points with a straight line.
c) Calculate the gradient of line AB.
11. The diagram below shows the line with equation3𝑥 + 2𝑦 = 18. Points A and B are the y-intercepts
and X-intercepts respectively. M is the mid-point of AB.
A
O
B
Find the co-ordinates of:
a) The point A
b) The point B
c) The point M