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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.

tusaale · line through (0,1) and (2,5)

Geometry · Coordinate-Geometry

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

0,\ 1,\ 2,\ 5

tallaabo tallaabo

  1. m = \frac{\Delta y}{\Delta x} = \frac{4}{2} = 2

    Slope = rise over run.

  2. y - 1 = 2(x - 0)

    Point-slope form through P.

  3. y = 2 x + 1

    Slope-intercept form.

Jawaabta muuji
y = 2 x + 1

Haddaad Dooro dhibaato, ama qoraal ama sawirkaaga. Talaab kasta, sawir, jawaabta qarsoon ilaa aad weydiiso.

Ku hay shaqadaada

A xisaab bilaash ah oo ku daray qoraalada waxbarasho kasta, diiwaanka waxa aad dhamaatay, dhibaatooyinka aad xal u tahay meel kaliya, iyo macallinka aad weydiisan kartaa oo ku saabsan bogga. Xisaabta oo keliya waa u furan yahay qof kasta, la diiwaan geliyey ama aan.

Ku soo biir Ku soo gal

Calaamadaha la isticmaalay halkan

Taab calaamad kasta oo loogu talagalay qeexidda buuxda, sawir, iyo waxa xarfaha oo dhan ka mid ah ka dhigan tahay.

Sida loo: Coordinate geometry

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

Su'aalaha dadku waydiiyaan

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.

In ka badan Geometry

TrianglesPythagorean theoremCirclesPolygonsSolidsEuclid's axioms and the structure of proofCongruent and similar trianglesCircle theoremsTransformations: translation, rotation, reflection, dilationSolid geometry: prisms, pyramids, spheres