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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.
דוגמה עובדת · line through (0,1) and (2,5)
צעד אחר צעד
- 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.
גלה את התשובה
עכשיו אתה בחר בעיה, או הקלד או צייר בעצמך. כל צעד, תמונה, התשובה חבויה עד שתשאל.
סמלים המשמשים כאן
הקש כל סמל להגדרה המלאה, תמונה, ומה כל אות בזה אומר.
איך: Coordinate geometry
- Slope = rise over run.
- Point-slope form through P.
- Slope-intercept form.
שאלות שאנשים שואלים
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.
יותר בפנים. Geometry
TrianglesPythagorean theoremCirclesPolygonsSolidsEuclid's axioms and the structure of proofCongruent and similar trianglesCircle theoremsTransformations: translation, rotation, reflection, dilationSolid geometry: prisms, pyramids, spheres