What are the x-coordinate and y-coordinate of the point of intersection of the two axes?
Step-by-step solution
Idea: The x-coordinate is the distance from the y-axis and the y-coordinate is the distance from the x-axis. The meeting point is on both axes, so both distances are 0.
- The point where the axes cross is the origin O. It lies on the y-axis, so its distance from the y-axis, its x-coordinate, is 0.½ mark
- It also lies on the x-axis, so its y-coordinate is 0. Hence O = (0, 0).½ mark
Check: Every point on the x-axis is (x, 0) and every point on the y-axis is (0, y); the only point of both forms is (0, 0) ✓.
Answer to write in the exam
The axes intersect at the origin O.
x-coordinate = 0, y-coordinate = 0
∴ O = (0, 0)
Common mistakes that cost marks
- Writing (1, 1), thinking the numbering starts at 1. The numbering on both axes starts at 0 at O.
- Saying the origin is in Quadrant I. It is on both axes, so it is in no quadrant.
- Giving only one number, “0”. A point needs both coordinates: (0, 0).
How this can come in the exam
The distance of the point (−8, 15) from the origin is
- 17 units
- 23 units
- 7 units
- 289 units
Show answer
(A) 17 units
√((−8 − 0)2 + (15 − 0)2) = √(64 + 225) = √289 = 17.
Assertion (A): The origin does not lie in any quadrant.
Reason (R): The origin lies on both axes, and points on the axes do not belong to any quadrant.
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is not the correct explanation of A.
- A is true but R is false.
- A is false but R is true.
Show answer
(A) Both A and R are true, and R is the correct explanation of A.
Quadrants are the four regions between the axes; points on the axes, including O, belong to none of them.
Try one yourself
Write the coordinates of the point where the axes meet, and of the point 3 units directly below it.
Show answer
(0, 0) and (0, −3).
More questions like this
- Point W has x-coordinate equal to −5. Can you predict the coordinates of point H which is on the line through W parallel to the y-axis? Which quadrants can H lie in?
- Consider the points R (3, 0), A (0, −2), M (−5, −2) and P (−5, 2). If they are joined in the same order, predict:
- Plot point Z (5, −6) on the Cartesian plane. Construct a right-angled triangle IZN and find the lengths of the three sides.
(Comment: Answers may differ from person to person.) - What would a system of coordinates be like if we did not have negative numbers? Would this system allow us to locate all the points on a 2-D plane?
- Are the points M (−3, −4), A (0, 0) and G (6, 8) on the same straight line? Suggest a method to check this without plotting and joining the points.