Coordinates

Coordinates are always written as (x, y) — the horizontal value first, then the vertical value. The memory trick is 'along the corridor, then up the stairs.'

Moving 5 steps to the right along the horizontal x-axis gives a positive value: $x=+5$.

Moving 2 steps down along the vertical y-axis gives a negative value: $y=-2$.

Putting x first and y second: the coordinate is (5, -2).

We need to convert a description of position — 5 right, 2 down — into a coordinate pair in the correct (x, y) format.

(-2, 5) puts the y-value first and the x-value second, which is the wrong order. Coordinates are always written x first, then y.

(5, 2) has the correct x-value but uses $y=+2$, meaning 2 steps up, not 2 steps down. Moving down means the y-value should be negative.

(-5, 2) uses a negative x-value, which would mean moving to the left, not to the right. This does not match the description.

(5, -2) correctly shows $x=5$ (right) and $y=-2$ (down), in the proper (x, y) order.

The Cartesian coordinate system is named after the French philosopher and mathematician René Descartes (1596–1650).

According to a popular story, Descartes came up with the idea while watching a fly walk across a tiled ceiling. He realised he could describe the fly's position using two numbers based on the tile grid.

The correct answer is René Descartes, inspired by watching a fly on a tiled ceiling.

The question asks for both the inventor and the inspiration behind the Cartesian coordinate system.

Isaac Newton and the falling apple is associated with the discovery of gravity, not the coordinate system. Newton is not credited with inventing coordinates.

Galileo Galilei studied planetary motion but did not invent the Cartesian coordinate system. The system is named after Descartes, not Galileo.

René Descartes, inspired by ships at sea names the right person but gives the wrong inspiration. The famous story involves a fly on a ceiling, not ships.

René Descartes, inspired by watching a fly on a tiled ceiling is correct on both counts — the right person and the right story.