COORDINATE GEOMETRY

Coordinate Geometry - Tough Revision Questions

1. Find the gradient of the line passing through (2, 5) and (7, 15).
2. Calculate the distance between the points A(1, 2) and B(4, 6).
3. Find the coordinates of the midpoint between (−3, 7) and (5, −1).
4. Determine the equation of the line with gradient 2 and passing through point (4, −3).
5. Is the triangle formed by points A(2, 1), B(6, 3), and C(4, 5) isosceles?
6. Find the equation of a line parallel to y = 3x − 4 and passing through (1, 2).
7. Find the coordinates of the point where the lines y = 2x + 1 and y = −x + 7 intersect.
8. Find the gradient and y-intercept of the line 4x − 3y = 9.
9. Find the equation of the perpendicular bisector of the line segment joining (−2, 3) and (4, −1).
10. Determine if the points (1, 2), (4, 3), and (7, 4) lie on the same straight line.
11. Find the distance between (−1, −1) and (2, 3).
12. Find the midpoint of the diagonal joining opposite vertices of rectangle with vertices (1, 1) and (5, 5).
13. Write the equation of the line passing through (3, 2) with an undefined gradient.
14. Find the gradient of a line perpendicular to y = −2x + 5.
15. If A(2, −1) and B(6, 3) are endpoints of a diameter of a circle, find the center.
16. Prove that the triangle with vertices (0, 0), (6, 0), and (3, 4) is a right-angled triangle.
17. Find the length of the diagonal of a square with vertices at (1, 1), (1, 5), (5, 5), and (5, 1).
18. Find the area of a triangle whose vertices are (1, 2), (4, 6), and (7, 2).
19. Determine if the quadrilateral with vertices (0, 0), (4, 0), (3, 3), and (−1, 3) is a parallelogram.
20. Find the coordinates of the centroid of triangle with vertices A(2, 3), B(4, 7), C(6, −1).
21. Find the equation of the line passing through points (2, 1) and (6, 5).
22. Find the x-intercept of the line 2x − y = 6.
23. Find the point that lies one-third of the way from (−6, 3) to (3, −3).
24. Determine the type of triangle formed by the points (0, 0), (2, 3), and (4, 0).
25. Find the equation of a line that is perpendicular to y = ½x + 4 and passes through (4, −2).
26. Find the length of the line segment between (a, b) and (−a, −b).
27. If a line has equation y = −x + 3, find the y-coordinate where it crosses the y-axis.
28. Show that points A(1, 1), B(3, 5), and C(5, 9) are collinear.
29. Find the gradient of the line joining (4, 5) and (−2, −1), and state if it's increasing or decreasing.
30. Find the coordinates of a point that divides the line segment from (−2, 1) to (4, 7) in the ratio 2:1.