Grade 10 - Coordinate Geometry Worksheet
1. Using the graph below, find and state the equation of each of the following lines below:
2. Find the equation of the straight line passing through
a. (1, 1) and (2, 5)
b. (6, 3) and (2, 6)
c. (3, 4) and with gradient 2
3
d. (1, −3) and with gradient − 4
e. (2, −3) and perpendicular to 𝑦 = 2𝑥 + 1
3.
A straight line is drawn through the points 𝐴(−5, 3) and 𝐵(1, 2).
a. Determine the gradient of AB
b. Write the equation of the line AB
4. The coordinates of A and B are (3, 5) and ( −1, − 3) respectively.
a. Find the gradient of the line AB
b. State the coordinates of the midpoint of A and B.
5. The line l passes through the points S(6, 6) and T(0, -2). Determine:
a. The gradient of the line l.
b. The equation of the line l.
6. A straight line HK cuts the 𝑦 − 𝑎𝑥𝑖𝑠 at (0, −1). The gradient of HK is
Show that the equation of the line HK is 2𝑥 − 3𝑦 = 3.
7. The coordinates of A and B are (3, 1) and (−1, 3) respectively.
a. Find the gradient of the line AB
b. State the coordinates of the midpoint of A and B
2
3
.
c. Hence determine the equation of the perpendicular bisector of AB
8.
The coordinates of the points A and B are (5, 24) and (−10, −12) respectively.
a. Calculate the gradient of the line joining A and B
b. Determine the equation of AB
c. State the coordinates of the 𝑦 − 𝑎𝑥𝑖𝑠 intercept for the line AB.
9. The points A, B, C have coordinates (3, −5), (4, −6) and (11, 1) respectively.
a. Show that AB is perpendicular to BC
b. Find the length of AC
c. Find the coordinates of the midpoint of AC.
10. A straight line is drawn through the points A(2, 1) and B(4, -3).
a. Calculate the gradient of the line AB.
b. Write the equation of the line AB.
CD is a line parallel to AB and passes through the origin.
c. Write the equation of the line CD.
d. Hence determine the equation of the perpendicular bisector of AB.
e. Calculate the gradient of a line perpendicular to CD.
11. P is the point (4, 2), Q is the point (12, 5) and R is the point (1, 3). Calculate:
a. The length of PR
b. The gradient of PQ
c. The equation of the line passing through R and parallel to PQ.
12. Three points have coordinates 𝐴 (−5, 6), 𝐵 (1, −4) and 𝐶 (3, 4). By calculation:
a. Show that the triangle is isosceles
b. Find the co-ordinates of the mid-point of the longest side.
13.
a. Find the equation of the line joining A ( −1, −9) to B,(6, 12).
b. Another line passes through C (7, −5) and meets AB at right angle at D. Find the
equation of CD and calculate the co-ordinates of D.
14. A straight line is drawn through the points A(1, 1) and B (5, −2).
a. Calculate the gradient of the line, AB
b. Write the gradient of any line that is perpendicular to AB.
c. Determine the equation of the line which passes through D (3, 2) and is
perpendicular to AB.
15. The graph below shows two straight lines 𝑙1 and 𝑙2 . Line 𝑙1 intercepts the y-axis at
(0, 1). Line 𝑙2 intercepts the 𝑥 and 𝑦 axes at (12, 0) and (0, 6) respectively.
a. Calculate the gradient of the lines 𝑙1 and 𝑙2
b. Determine the equation of 𝑙1
c. What is the relationship between lines 𝑙1 and
𝑙2 . Give a reason for your answer.
16. The diagram below shows the two points 𝐴(6, 7) and 𝐵(3, 2).
a.
b.
c.
d.
Calculate the gradient of AB
Calculate the length of the line segment AB
Determine the equation of the line AB
Obtain the value of 𝑥, if a point 𝑃(𝑥, −6) lies on AB.