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Coordinate geometry

Distance, midpoint, slope and the equation of a line.

Coordinates turn geometry into algebra. The distance between two points is Pythagoras; the midpoint is an average; the slope is rise over run; and slope plus a point gives the line's equation.

例題 · line through (0,1) and (2,5)

Geometry · Coordinate-Geometry

Line through (0,1) and (2,5)

0,\ 1,\ 2,\ 5

ステップバイステップ

m = \frac{\Delta y}{\Delta x} = \frac{4}{2} = 2
Slope = rise over run.
y - 1 = 2(x - 0)
Point-slope form through P.
y = 2 x + 1
Slope-intercept form.

答えを表示

y = 2 x + 1

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どうやって: Coordinate geometry

Slope = rise over run.
Point-slope form through P.
Slope-intercept form.

よくある質問

Why does every triangle have angles adding to 180°?

Draw a line through one vertex parallel to the opposite side: the two alternate angles equal the other two angles of the triangle, and the three angles at the vertex lie on a straight line. That is Euclid's proof, and it is why the fact holds only on a flat plane.

When do I use the law of sines versus the law of cosines?

Cosines when you know three sides, or two sides and the angle between them. Sines when you know an angle and the side opposite it, plus one more piece.

What is the difference between area and perimeter?

Perimeter is the length of the boundary (one dimension, measured in metres); area is the amount of surface inside (two dimensions, square metres). Doubling every side doubles the perimeter but quadruples the area.

More in Geometry

Triangles Pythagorean theorem Circles Polygons Solids Euclid's axioms and the structure of proof Congruent and similar triangles Circle theorems Transformations: translation, rotation, reflection, dilation Solid geometry: prisms, pyramids, spheres