Coordinate geometry — plotting points and travel graphs

The origin is the special point where the x-axis and the y-axis cross each other. It is labelled O on the number plane.

At the origin, there is no movement along the x-axis and no movement along the y-axis. This means both the x-coordinate and y-coordinate are zero.

Since $x=0$ and $y=0$, the coordinates of the origin are written as (0, 0).

We need to find the coordinates of the origin — the point where both axes meet.

The point (1, 1) is 1 unit to the right and 1 unit up from the origin — it is not the origin itself.

The point (0, 1) lies on the y-axis but 1 unit above the origin, and (1, 0) lies on the x-axis but 1 unit to the right. Neither is the crossing point of both axes.

The origin is where both axes cross, so both coordinates must be zero. The correct answer is (0, 0).

Moving right from the origin gives a positive x-coordinate. Moving downward from the x-axis gives a negative y-coordinate.

Moving 5 units to the right means $x=+5$. Moving 3 units downward means $y=-3$.

Coordinates are always written as $(x,y)$, so the point is (5, −3). Remember: x-coordinate first, then y-coordinate.

We need a point that is 5 to the right (positive x) and 3 downward (negative y). The correct form is $(+5,-3)$.

The point (−5, 3) is 5 units to the left and 3 units up — the opposite of what was described.

The point (3, −5) has the numbers swapped — it moves 3 right and 5 down, not 5 right and 3 down.

The point (5, 3) is 5 right and 3 up, but the description says downward, so the y-coordinate must be negative.

The only option matching 5 right and 3 down is (5, −3).