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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.

कार्यरत उदाहरण · line through (0,1) and (2,5)

Geometry · Coordinate-Geometry

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

0,\ 1,\ 2,\ 5

चरणानुक्रमे

  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.

उत्तर उघडा
y = 2 x + 1

आता तुम्ही प्रश्न निवडा, किंवा स्वतःचा प्रश्न टाइप करा किंवा रेखाटून दाखवा. प्रत्येक टप्प्यात, चित्रे आहेत, तुम्ही विचारण्याआधी उत्तर लपवलेले आहे.

स्वतःचे कार्य चालू ठेवा

मोफत खाते प्रत्येक शिकवणी वर टिपण्णी जोडते, तुम्ही पूर्ण केलेल्या गोष्टीचा नोंदवही, तुमच्या सोडविलेल्या समस्या एका ठिकाणी, आणि या पानाच्या विषयी तुम्ही विचारू शकता अशा शिक्षकाला. गणित स्वतःच सर्वांसाठी खुले आहे, दाखलन झालेले असो किंवा नसो.

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कसे कराल: Coordinate geometry

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

लोक विचारतात ते प्रश्न

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.

अधिक माहिती Geometry

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