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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.

Kugwira ntchito chitsanzo · line through (0,1) and (2,5)

Geometry · Coordinate-Geometry

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

0,\ 1,\ 2,\ 5

Gawo ndi Gawo

  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.

Kusonyeza yankho
y = 2 x + 1

Tsopano inu Sankhani vuto, kapena kulemba kapena kujambula wanu. Pakalipano, yankho limeneli lidzapezeka patsamba lino.

Kusunga ntchito yanu yokha

M’malo mwake, maakaunti aulere amawonjezera malemba pazophunzira zonse, mnda wa zomwe mwamaliza, mavuto anu omaliza m’malo limodzi, ndi m’bale amene mungafunse za nkhaniyo. Maphunziro a matekinoloje ndi otsegulira kwa aliyense, olembetsa kapena osalembetsa.

Kulembetsa Kulowa

Zithunzi

Pitani pa dzina lililonse lachifaniziro kuti mudziwe tanthauzo lake, chithunzi chake, ndi zimene limatanthauza.

Momwe mungagwiritsire ntchito: Coordinate geometry

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

Mafunso omwe anthu amafunsa

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.

Zambiri pa Geometry

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