Coordinate Geometry – Straight Lines Quiz - ICSE Class 11 Mathematics

Free practice quiz: Coordinate Geometry – Straight Lines (ICSE Class 11 Mathematics). 51 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 11 Mathematics practice quiz has 51 multiple-choice questions on Coordinate Geometry – Straight Lines, and 51 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. The equation of a straight line passing through the origin and inclined at an angle of 135 degrees with the positive x-axis is:

   1. y = x
   2. y = -x
   3. x + y = 0
   4. y = x + 1
   Show answer

   Answer: B. y = -x

   The angle of inclination is 135 degrees. The slope 'm' of a line is given by tan(theta). So, m = tan(135) = tan(180 - 45) = -tan(45) = -1. The equation of a line passing through the origin (0,0) with slope 'm' is y = mx. Therefore, y = -1*x, which simplifies to y = -x.

2. The lines 3x + 4y - 7 = 0 and 4x - 3y + 5 = 0 are:

   1. Parallel
   2. Perpendicular
   3. Identical
   4. Intersecting at (1,1)
   Show answer

   Answer: B. Perpendicular

   The slope of the first line 3x + 4y - 7 = 0 is m1 = -3/4. The slope of the second line 4x - 3y + 5 = 0 is m2 = -4/-3 = 4/3. The product of their slopes is m1 * m2 = (-3/4) * (4/3) = -1. Since the product of the slopes is -1, the lines are perpendicular.

3. Find the equation of the line passing through the origin and perpendicular to the line joining the points (2, 3) and (4, 5).

   1. x + y - 0 = 0
   2. x - y + 0 = 0
   3. x + y - 1 = 0
   4. x - y + 1 = 0
   Show answer

   Answer: A. x + y - 0 = 0

   First, find the slope of the line joining (2, 3) and (4, 5). m1 = (5 - 3) / (4 - 2) = 2 / 2 = 1. The slope of a line perpendicular to this line is m2 = -1/m1 = -1/1 = -1. The line passes through the origin (0, 0) and has a slope of -1. Using the point-slope form y - y1 = m(x - x1): y - 0 = -1(x - 0) => y = -x. Rearranging this equation gives x + y = 0.

4. Find the equation of the line passing through (1, 3) and parallel to the line y = 2x + 5.

   1. y = 2x + 1
   2. y = 2x - 1
   3. 2x - y + 1 = 0
   4. 2x - y - 1 = 0
   Show answer

   Answer: A. y = 2x + 1

   The given line is y = 2x + 5. Its slope is m = 2. A line parallel to this will have the same slope, m = 2. The equation of a line passing through (1, 3) with slope 2 is y - 3 = 2(x - 1) => y - 3 = 2x - 2 => y = 2x + 1.

5. The equation of the line passing through (0, 0) and (a, b) is:

   1. bx - ay = 0
   2. ax - by = 0
   3. bx + ay = 0
   4. ax + by = 0
   Show answer

   Answer: A. bx - ay = 0

   The slope of the line passing through (0, 0) and (a, b) is m = (b - 0) / (a - 0) = b/a (assuming a != 0). The equation of the line passing through the origin with slope m is y = mx. So, y = (b/a)x. Multiplying by a gives ay = bx. Rearranging this equation gives bx - ay = 0.

More questions in this quiz

Answers and explanations are in the full quiz.

1. Find the equation of the line passing through the point (2, 3) and parallel to the line 3x - 4y + 5 = 0.
2. The lines ax + by + c = 0 and bx - ay + d = 0 are:
3. The angle between the lines y = (2 - sqrt(3))x + 1 and y = (2 + sqrt(3))x - 2 is:
4. Find the equation of the line passing through the point (-1, 2) and perpendicular to the line 2x + 3y - 5 = 0.
5. The lines x = a and y = b intersect at the point:
6. The equation of the line passing through (x1, y1) and (x2, y2) is:
7. If a line makes an angle of 60 degrees with the positive x-axis, its slope is:
8. The equation of a line parallel to the y-axis is of the form:
9. Find the equation of the line passing through (3, -2) and parallel to the x-axis.
10. Find the y-intercept of the line 2x + 5y - 10 = 0.
11. The equation of the line passing through the origin and having a slope of -2/3 is:
12. The lines ax + by + c = 0 and Ax + By + C = 0 are parallel if:
13. Find the equation of the line passing through (1, -1) and (3, 5).
14. The equation of the line perpendicular to ax + by + c = 0 and passing through (x1, y1) is:
15. Find the x-intercept of the line 4x - 5y + 20 = 0.
16. The equation of the line passing through (2, 3) and having an undefined slope is:
17. The angle between the line y = mx + c and the x-axis is given by:
18. The equation of the line passing through the point (a, b) and parallel to the line Ax + By + C = 0 is:
19. The lines x = 5 and y = -3 intersect at the point:
20. Find the distance between the parallel lines 3x + 4y - 5 = 0 and 3x + 4y + 10 = 0.
21. The equation of the line passing through (1, 2) and perpendicular to the line x - 2y + 3 = 0 is:
22. If the lines y = m1x + c1 and y = m2x + c2 are perpendicular, then:
23. Find the equation of the line passing through the point (3, 4) and making an angle of 135 degrees with the positive x-axis.
24. The foot of the perpendicular from the origin to the line 3x + 4y - 25 = 0 is:
25. The lines x = c and y = c are:
26. Find the equation of the line passing through (5, 2) and parallel to the line 2x + y - 7 = 0.
27. The angle between the lines y = x and y = -x is:
28. The equation of the line passing through (2, 2) and (4, 4) is:
29. Find the equation of the line passing through (5, -1) and perpendicular to the line 3x + 2y - 6 = 0.
30. The equation of the line passing through the origin and making an angle of 45 degrees with the positive x-axis is:
31. Find the value of k if the lines 5x - 2y + 3 = 0 and kx + 4y - 1 = 0 are parallel.
32. The equation of the line passing through (1, 2) and (1, 5) is:
33. Find the equation of the line passing through (-2, 3) and parallel to the x-axis.
34. The lines ax + by + c = 0 and Ax + By + C = 0 are identical if:
35. Find the equation of the line passing through (1, 1) and perpendicular to the line x + y + 1 = 0.
36. The y-intercept of the line passing through (3, 4) and (5, 6) is:
37. Find the equation of the line passing through (4, -1) and parallel to the line 3x - y + 5 = 0.
38. The lines x = a and y = b are:
39. Find the equation of the line passing through (2, 3) and perpendicular to the line 3x + 4y - 5 = 0.
40. The equation of the line passing through (-1, -2) and making an angle of 45 degrees with the positive x-axis is:
41. Find the equation of the line passing through the origin and perpendicular to the line 2x - 3y + 4 = 0.
42. The equation of the line passing through (a, b) and parallel to the y-axis is:
43. Find the equation of the line passing through (1, 1) and (3, 3).
44. The lines ax + by + c = 0 and Ax + By + C = 0 are perpendicular if:
45. Find the equation of the line passing through (3, -2) and perpendicular to the line y = (1/2)x + 3.
46. The equation of the line passing through the origin and making an angle of 135 degrees with the positive x-axis is:

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