MCQ in Analytic Geometry: Points, Lines and Circles Part 1 – Answers

MCQ in Analytic Geometry: Points, Lines and Circles Part 1 Answer Key | Mathematics Board Exam

You have worked through Part 1 of the Analytic Geometry MCQ Series on points, lines and circles. Now this is where your review gets more valuable.

This answer key covers every item in the first set, compiled from past board exam problems, engineering mathematics textbooks, academic journals, and other references that serious reviewees have used to prepare for the Mathematics section of the board exam. The answers are here to help you do more than just confirm what you got right. They are here to show you clearly where your understanding is solid and where it still has room to grow.

Analytic geometry problems on the board exam are precise. A misread coordinate, a wrong sign, or a confused formula can send an entire solution in the wrong direction while still looking correct on paper. That is why going through this answer key carefully matters more than just counting your score.

For every item you got wrong, go back to the question and work through the correct solution from the beginning. Do not just look at the answer and accept it. Trace the full reasoning, find the point where your approach went off, and understand what the correct method actually looks like. That process is what makes review sessions productive instead of just time consuming.

If you came here without attempting the questions first, go back to Part 1 and do the work. The answer key only earns its value after you have genuinely tried every problem on your own.

Check every answer, study every mistake, and bring what you learn into Part 2.

1. B. 21

Solution: What is the linear distance between –4 and 17 on the number line?

2. C. 10

Solution: If the distance between points (3, y) and (8, 7) is 13, then what is y?

3. D. –5 or 19

Solution: If the distance between points (3, y) and (8, 7) is 13, then what is y?

4. C. (3, -3)

Solution: Find the coordinate of a point equidistant from (1, -6), (5, -6) and (6, -1)

5. C. 5, 0

Solution: The line segment connecting (x, 6) and (9, y) is bisected by the point (7, 3)

6. B. x = -10, y = –1

Solution: If (-2, -4) is the midpoint of (6, -7) and (x, y), what are x and y?

7. A. (-1, 1)

Solution: Determine the coordinates of the point which is three-fifths of the way

8. D. (11, -20)

Solution: What is the terminal point of a line segment extending three times its own length?

9. B. c – b = b – a

Solution: The points (a, 1), (b, 2) and (c, 3) are collinear. Which of the following is true?

10. D. 8

Solution: Find the abscissa of P if its ordinate is 6

11. B. 14.93°

Solution: Find the inclination of the line passing through (-5, 3) and (10, 7)

12. C. 45º

Solution: Find the angle formed by the lines 2x+y–8=0 and x+3y+4=0

13. B. 11º 19’

Solution: Find the angle between the lines 3x+2y=6 and x+y=6

14. A. 4.4º

Solution: What is the acute angle between the lines y=3x+2 and y=4x+9?

15. D. 1

Solution: Find the distance of the line 3x+4y=5 from the origin

16. B. (64, -44) and (4, -4)

Solution: What are the two points on the line which are at a distance 2 units from another line?

17. B. 2

Solution: What is the distance from the point (2, 1) to the line 4x–3y+5=0?

18. B. 3.54

Solution: Determine the distance from (5, 10) to the line x-y=0

19. B. 5 units

Solution: What is the distance from a point (1, 3) to the line 4x+3y+12=0?

20. B. 4

Solution: Find the distance between the given lines 4x-3y=12 and 4x-3y=-8

21. D

Solution: Find the distance between the lines, 3x+y-12=0 and 3x+y-4=0

22. A. 10

Solution: What is the length of the line with a slope of 4/3 from a point (6, 4) to the y-axis?

23. A. 1

Solution: Find the slope of the line defined by y-x=5

24. C. -3/2

Solution: What is the slope of the line 3x+2y+1=0?

25. B. 9 sq. units

Solution: What is the area of the triangle given the points of the vertices?

26. B. 4

Solution: Find the area of the triangle given the points of the vertices?

27. C. 25 sq. units

Solution: What is the area of the square given the points of the vertices?

28. B. y = -x – 2

Solution: Find the equation of the line passing thru (1, -3) and (-4, 2) in slope-intercept form

29. B. 5

Solution: What is the x-intercept of the line passing through (1, 4) and (4, 1)?

30. B. 3x – y + 1 = 0

Solution: Find the equation of the straight line with a slope of 3 and a y-intercept of 1

31. D. 2x + y + 1 = 0

Solution: If the points (-2, 3), (x, y) and (-3, 5) lie on a straight line, then what is the equation of the line?

32. C. 3x – 2y = 12

Solution: What is the equation of a line that intercepts the x-axis at x=4 and the y-axis at y=-6?

33. C. 8

Solution: Solution: What is the x-coordinate of a point on the line if its corresponding y-coordinate is 6?

34. A. y – 6x = 0

Solution: Find the equation of the line passing through the origin and with a slope of 6?

35. B. y + 2x – 4 = 0

Solution: Find the equation of the line if the x-intercept and y-intercept are -2 and 4

36. C. 3

Solution: Determine B such that 3x+2y–7=0 is perpendicular to 2x–By+2=0

37. B. -3/2

Solution: The line 2x–3y+2=0 is perpendicular to another line L1 of unknown equation

38. C. –6

Solution: A line through (-5, 2) and (1, -4) is perpendicular to the line through (x, -7) and (8, 7).

39. C. x – y – 4 = 0

Solution: What is the equation of the line that passes thru (4, 0) and is parallel to the line x–y–2=0?

40. B. 5x – y = 14

Solution: Find the equation of the line through point (3, 1) and is perpendicular to the line x+5y+5=0

41. B. 8x – 2y + 11 = 0

Solution: Find the equation of the perpendicular bisector of the line joining (5, 0) and (-7, 3)

42. D. 15 x – 10y – 9 = 0

Solution: Which of the following lines is parallel to the line 3x–2y+6=0?

43. A. 7x + 2y + 31 = 0

Solution: What is the equation of the line through (-3, -5) parallel to 7x+2y–4=0?

44. C. 4x + 5y = 2

Solution: What is the equation of the line joining the points (3, -2) and (-7, 6)?

45. D. 2x + y – 2 = 0

Solution: What is the equation of the line passing through (-2, 6) with the x-intercept half the y-intercept?

46. D. –3

Solution: Find the slope of a line having a parametric equation of x=2+t and y=5–3t

47. D. 4

Solution: Find the slope of the line having a parametric equation y=4t+6 and x=t+1

48. D. x – 4y = –14

Solution: What is the locus of the third vertex of a triangle?

49. A. 3

Solution: Find the area of the triangle which the line 2x–3y+6=0 forms with the coordinate axis

50. B. 2x – y – 2 = 0

Solution: Find the equation of the line given the length of the line segment

Online Questions and Answers in Analytic Geometry: Points, Lines and Circles Series

Following is the list of practice exam test questions s in this brand new series: