Where's the Point?

Drag the sliders to move the dot and watch its address on the line — or the plane — update live.

x = 0

at the origin

x value

OriginThe point 0 is called the origin — the starting mark every distance is measured from.

Positive sideSlide right and x grows — every point to the right of 0 is positive.

Negative sideSlide left and x shrinks below 0 — every point to the left is negative.

A number line only needs ONE number to say exactly where a point is.

P = (0, 0)

at the origin

x-axis →

y-axis ↑

Origin O = (0,0)Where the x-axis and y-axis cross. Every point is measured from here.

Quadrant I (+, +)Top-right. Both x and y are positive.

Quadrant II (−, +)Top-left. x is negative, y is positive.

Quadrant III (−, −)Bottom-left. Both x and y are negative.

Quadrant IV (+, −)Bottom-right. x is positive, y is negative.

Dashed linesDrop straight down to the x-axis and across to the y-axis — those two numbers are the coordinates.

A coordinate plane needs TWO numbers, (x, y), to say exactly where a point is.

Point A

Point B

Horizontal leg (Δx)

Vertical leg (Δy)

Distance (hypotenuse)

A = (-3, -2)

B = (4, 3)

d ≈ 0

-3

-2

d = √( (x₂ − x₁)² + (y₂ − y₁)² )

d = √( (7)² + (5)² )

d = √( 49 + 25 )

d = √74

d ≈ 8.6

Horizontal legMove from A to B along x only: Δx = x₂ − x₁. This is one leg of a right triangle.

Vertical legMove from B's x-line up to B along y only: Δy = y₂ − y₁. This is the other leg.

Pythagoras does the restThe segment AB is the hypotenuse, so d² = Δx² + Δy² — just like any right triangle.

Drag any slider and watch the right triangle — and the formula below it — update together.

Score: 0 / 0

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