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9709 Pure 1 · 1.3 Coordinate Geometry

The Line Lab

Drag A and B, or type in the points from your homework. Every answer below is exact and the working is written out, so you can check your own answer one step at a time.

Snap to

Drag a point, or press Tab to reach it and move it with the arrow keys.

The points

Type whole numbers or halves, like 3, −2, 2.5 or 7/2.

Gradient of AB
Midpoint of AB
Length of AB
Equation of line AB
y − y₁ = m(x − x₁), with A
y = mx + c
ax + by + c = 0
How do I get the integer form?

    Which form does the question want? When a question says "in the form ax + by + c = 0", the coefficients must be whole numbers. Leaving a fraction in costs the mark, so clear the fractions first and then move everything to one side.

    Perpendicular gradients. Two lines are perpendicular when their gradients multiply to −1. Flip the fraction and change the sign: 2/3 becomes −3/2. A horizontal line and a vertical line are perpendicular too, even though the vertical one has no gradient.

    Straight Lines lesson All math