Reflection (In x-axis, y-axis, x = a, y = a and the origin; Invariant Points)

294. Coordinates & Axes · Finding your place on the plane

P's coordinates match its distance from the axes.

A point's coordinates measure its perpendicular distances from the axes — the x-coordinate from the y-axis and the y-coordinate from the x-axis, each signed by direction. Together they pin the point exactly.

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For subscribers · Selina ICSE: Reflection (In x-axis, y-axis, x = a, y = a and the origin; Invariant Points)

What this lesson covers

Try to break it

Drag P anywhere. The dashed lines from P show its perpendicular distances to the two axes — those distances are the coordinates (x, y), signed by the quadrant. Pull P onto an axis and one dashed line collapses to length 0; pull P to the origin and both do.

How you build it

Plot point P on the coordinate plane.

Place point P in the first quadrant.

The proof, step by step

Prove that the coordinates of P give its distances from the axes.

The first number in the pair (x, y) is the abscissa.
The second number in the pair (x, y) is the ordinate.
Abscissa is the distance from the y-axis.
Ordinate is the distance from the x-axis.

Worked example

In the Cartesian plane, if a point P has coordinates (4, -3), what are its abscissa and ordinate respectively?

The abscissa is the first coordinate (x-value), which is 4. The ordinate is the second coordinate (y-value), which is -3.

Abscissa: 4, Ordinate: -3 — correct
Abscissa: -3, Ordinate: 4
Abscissa: 4, Ordinate: 3
Abscissa: -3, Ordinate: -3