Meta lesson: enter the rivnyannya stake, navchit scholars to store the rivnyannya stake for the preparation of the armchairs, there will be a number for the given rivnyannya.
Ustatkuvannya: Interactive board.
Lesson plan:
- Organizational moment - 3 min.
- Repetition. Organization of missed activity - 7 min.
- Explanation of the new material. Vysnovok Rivnyannya stake - 10 min.
- Closing the grape material - 20 min.
- Pidsumok for a lesson - 5 min.
Go to lesson
2. Repetition:
− (Dodatok 1 Slide 2) write down the formula for the values of the coordinates of the middle of the output;
− (Slide 3) W Describe the formula between dots
3. Explanation of the new material.
(Slide 4 - 6) Date of registration of the stake. Vive rivnyannya kola with a center at the point ( a;b) і with the center on the cob of coordinates.
(NS – a ) 2 + (at – b ) 2 = R 2 - Rivnyannya cola with the center Z (a;b) , radius R , NS і at – coordinates of the current stake point .
NS 2 + at 2 = R 2 - pivnyannya kola with center on the cob of coordinates.
(Slide 7)
In order to make a cup of flat stakes, you need:
- the nobility coordinate the center;
- the nobility dovzhinu radius;
- submit the coordinates to the center of the radius in the rivnyannya cola.
4. Razv'yazannya tasks.
For problems No. 1 - No. 6, place the stakes behind the ready-made chairs.
(Slide 14)
№ 7. Save the table.
(Slide 15)
№ 8. Stay in a stake, given by the women:
a) ( NS – 5) 2 + (at + 3) 2 = 36;
b) (NS + 1) 2 + (at– 7) 2 = 7 2 .
(Slide 16)
№ 9. Know the coordinates of the center of the AB- Cola diameter.
| Given: | Decision: | ||
| R | Coordinate center | ||
| 1 | A(0 ; -6) Have(0 ; 2) |
AB 2 = (0 – 0) 2 + (2 + 6) 2 ; AB 2 = 64; AB = 8 . |
A(0; -6) Have(0 ; 2) Z(0 ; – 2) – Centre |
| 2 | A(-2 ; 0) Have(4 ; 0) |
AB 2 = (4 + 2) 2 + (0 + 0) 2 ; AB 2 = 36; AB = 6. |
A (-2;0) Have (4 ;0) Z(1 ; 0) – Centre |
(Slide 17)
№ 10. Put the pivot point with the center on the cob of coordinates, but pass through the point Before(-12;5).
Decision.
R 2 = OK 2
= (0 + 12) 2 +
(0 – 5) 2 = 144 + 25 = 169;
R = 13;
Rivnyannya stake: x 2 + y 2 = 169 .
(Slide 18)
№ 11. Store the stakes, pass through the cob of coordinates from the center at the point Z(3; - 1).
Decision.
R 2 = OS 2 = (3 – 0) 2 + (–1–0) 2 = 9 + 1 = 10;
Rivnyannya stake: ( NS - 3) 2 + (y + 1) 2 = 10.
(Slide 19)
№ 12. Store the food cola in the center A(3; 2), go through Have(7;5).
Decision.
1. Center stake - A(3;2);
2.R = AB;
AB 2 = (7 – 3) 2 + (5 – 2) 2 = 25; AB
= 5;
3. Rivnyannya stake ( NS – 3) 2 + (at − 2) 2
= 25.
(Slide 20)
№ 13. Reverse, chi lie specks A(1; -1), Have(0;8), Z(-3; -1) for the number given by the equivalents ( NS + 3) 2 + (at − 4) 2 = 25.
Decision.
I... Acceptable point coordinates A(1; -1) in an equal stake:
(1 + 3) 2 +
(−1 − 4) 2 =
25;
4 2 + (−5) 2 = 25;
16 + 25 = 25;
41 = 25 - the parity is incorrect, it means A(1; -1) do not lie on the number given by the equal ( NS + 3) 2 +
(at −
4) 2 =
25.
II... Acceptable point coordinates Have(0; 8) in an equal stake:
(0 + 3) 2 +
(8 − 4) 2 =
25;
3 2 + 4 2 = 25;
9 + 16 = 25;
Have(0;8)lie down NS + 3) 2 +
(at − 4) 2
=
25.
ІІІ. Acceptable point coordinates Z(-3; -1) in an equal stake:
(−3 + 3) 2 +
(−1− 4) 2 =
25;
0 2 + (−5) 2 = 25;
25 = 25 - parity virna, meaning Z(-3; -1) lie down on the number given by the equal ( NS + 3) 2 +
(at − 4) 2
=
25.
Pidsumok lesson.
- Repeat: Rivnyannya stake, Rivnyannya stake with center on the cob of coordinates.
- (Slide 21) Homework.
Colom to be called a pointless point of the area, rivnoviddalenyh from the center of a point, which is called a center.
If point C is the center of the stake, R is the її radius, and M is the point of the stake, then after the value of the stake
Equality (1) є Rivnyannya cola radius R із center at point С.
Go on the square, a rectangular Cartesian coordinate system (Fig. 104) and point C ( a; b) - Center of stake radius R. Nekhai M ( NS; at) is a pretty good point of the whole stake.
Oskilki | CM | = \ (\ sqrt ((x - a) ^ 2 + (y - b) ^ 2) \), then equal (1) can be written as follows:
\ (\ sqrt ((x - a) ^ 2 + (y - b) ^ 2) \) = R
(x - a) 2 + (y - b) 2 = R 2 (2)
Rivnyannya (2) name to the home of the stake or for the stakes of the radius R centered at the point ( a; b). For example, rivnyannya
(x - l) 2 + ( y + 3) 2 = 25
є Rivnyannya stake of radius R = 5 і from the center at point (1; -3).
When the center of the stake is zbіgaєa with a cob of coordinates, then іvnyannya (2) swagger
x 2 + at 2 = R2. (3)
Rivnyannya (3) name stake canon .
Zavdannya 1. Write the line of the radius R = 7 with the center on the cob of coordinates.
Without pre-setting the value of the radius in rivnyannya (3) otrimaєmo
x 2 + at 2 = 49.
Zavdannya 2. Write the line of the radius R = 9 with the center at point C (3; -6).
Submitting the value of the coordinates of the point C and the value of the radius y to the formula (2), we can
(NS - 3) 2 + (at- (-6)) 2 = 81 or ( NS - 3) 2 + (at + 6) 2 = 81.
Zavdannya 3. Know the center and radius cola
(NS + 3) 2 + (at-5) 2 =100.
Rivnyuchi dane іf іs out-of-house іvnyаnnya cola (2), bachimo, scho a = -3, b= 5, R = 10. From the same, C (-3; 5), R = 10.
Zavdannya 4. Bring, oh rivnyannya
x 2 + at 2 + 4NS - 2y - 4 = 0
є Rivnyannyam stake. Know її center and radius.
Reconstruct a part of the ts'i rivnyannya:
x 2 + 4NS + 4- 4 + at 2 - 2at +1-1-4 = 0
(NS + 2) 2 + (at - 1) 2 = 9.
Tse rivnyannya є rivnyannyam kola centered at points (-2; 1); radius cola door 3.
Zavdannya 5. Write an equal number with a center at point C (-1; -1), but go straight AB, like A (2; -1), B (- 1; 3).
Let's write straight AB:
or 4 NS + 3y-5 = 0.
Oskilki may be in a straight line, then the radius of the conduction to the point of the torsion, perpendicular to the straight line. To display the radius, you need to know the distance from point C (-1; -1) - the center of the stake to straight 4 NS + 3y-5 = 0:
Let's write a ryvnyannya shukany cola
(x +1) 2 + (y +1) 2 = 144 / 25
Go to the straight-line coordinate systems dane colo x 2 + at 2 = R2. The point M ( NS; at) (fig. 105).
Come on radius vector OM> points M will set the value t with positive direct axis NS, until the abscissa and ordinate of point M change in fallowness from t
(0 t x i y through t, we know
x= R cos t ; y= R sin t , 0 t
Rivnyannya (4) called parametric equal numbers with the center on the cob of coordinates.
Zavdannya 6. The environment is set by the people
x= \ (\ sqrt (3) \) cos t, y= \ (\ sqrt (3) \) sin t, 0 t
Write down the canonical rіvnyannya tsyogo stake.
Wash the whimperє x 2 = 3 cos 2 t, at 2 = 3 sin 2 t... Stocking prices by term, will be accepted
x 2 + at 2 = 3 (cos 2 t+ sin 2 t)
abo x 2 + at 2 = 3
Analytical geometries give, however, the development of geometric structures. For all the given points and lines are brought to the same coordinate system.
In a coordinate system, it is possible to characterize a skin point with coordinates, and a skin line - as two unidentified ones, a graph like a line є. This rank geometrically to be built up to algebraic, de kindly, all priyomi numbered.
Circumference є geometric center of points with one singing power(The skin point of the stake is equal to one point, called the center). Rivnyannya kola can represent power, satisfy mind.
The geometric interpretation of the stake is the purpose of the stake.
If you place the stake in the coordinate system, then all the points of the stake will be satisfied with the same mind - we will see them to the center of the stake, but we will be the same and equal to the stake.
Colo centered at point A that radius R according to the coordinate area.
Yaksho coordinate center (a; b) , and the coordinates of the stake point (x; y) , then іvnyannya kola maє viglyad:
As the square of the radius of the stake is the same as the sum of the squares, the difference in the coordinates of whether the point of the stake is to the center, the price is equal to the level of the stake in the plane coordinate system.
If the center of the stake is zbіgayt from the point of the cob of coordinates, then the square of the radius of the stake is to the sum of the squares of the coordinates of any point of the stake. I have a vipad of іvnyannya cola nabuvaє viglyadu:
Otzhe, be-yaka geometric figure as a geometrical place of points, it starts with equal coordinates, which call the coordinates of the points. І navpaki, rіvnyannya, scho zv'yazuє coordinates NS і at , Viznachayut a line as a geometric place of points of the area, the coordinates of which are satisfied with the given line.
Apply the solution of the tasks of the Rivnyannya stake
Zavdannya. The table of the given stake
Store the farmhouse in the center at point O (2; -3) and radius 4.Decision.
Festering up to the formula of the ryvnyannya cola:
R 2 = (x-a) 2 + (y-b) 2
The formula is admittedly significant.
Radius cola R = 4
Coordinate the center of the stake
a = 2
b = -3
Otrimuєmo:
(x - 2) 2 + (y - (-3)) 2 = 4 2
abo
(x - 2) 2 + (y + 3) 2 = 16.
Zavdannya. Chi lay the point of the stake
Revision, where to trace the point A (2; 3) Rivnyannyu cola (x - 2) 2 + (y + 3) 2 = 16 .Decision.
The point is to trace the stake, the coordinates are satisfied with the equal circle.
To reconsider, where to locate the stake point from the given coordinates, it is assumed the coordinates of the point in the value of the given stake.
In rivnyannya ( x - 2) 2 + (y + 3) 2 = 16
Apparently, behind the sink, the coordinates of point A (2; 3), tobto
x = 2
y = 3
Revise the truth of good value
(x - 2) 2 + (y + 3) 2 = 16
(2
- 2) 2 + (3
+ 3) 2 = 16
0 + 36 = 16 unevenness
In such a rank, given point do not lay to the given stake.
Value 1. Numerical vissyu ( number straight line, coordinate line) Ox is called a straight line, at the point O is reversed by cob (cob of coordinates)(fig. 1), straight
O → x
said yak positive straightforwardness if it was determined as a result, if it was accepted for one dojini.
Value 2. Vidrizok, dozhina which is taken as a unit of dozhini is called a scale.
Skin point of the numerical axis MA coordinate speech number... The coordinate of point O is road to zero. Coordinate of the current point A, which lies on the Ox promenade, the road to the top OA. The coordinate of the current point A of the numerical axis, but not to lie on the Ox walk, is negative, but by its absolute value it is OA.
Value 3. The rectangular Cartesian coordinate system Oxy in the area name two together perpendicular numerical axes Ox i Oy s the same scaleі on the cob to see at point O, moreover, such that the turn from the Ox exchange to the corner 90 ° before the Oy exchange go right against the course of the year's shooting(Fig. 2).
Respect. The rectangular Cartesian coordinate system Oxy, shown in little 2, is called right coordinate system, on vidminu vid any coordinate systems, In which the turn of the Ox exchange to the cue 90 ° before the Oy exchange, go right in the direction of the old street. Have a friend of mine can only be viewed without the right coordinate systems, do not negotiate especially.
If on the square you enter the system of rectangular Cartesian coordinates Oxy, then the skin point of the square is two coordinates – abscissaі ordinate, scho counted offensive rank. Nekhai A is a good point of the area. Opportunity from point A perpendiculars AA 1 that AA 2 on a straight line Ox and Oy as an example (Fig. 3).
Value 4. The abscissa of point A is called the coordinate of the point A 1 on the numerical axis Ox, the ordinate of point A is called the coordinate of the point A 2 on the numerical axis Oy.
Designation. Coordinate (abscissa and ordinate) of a point A for rectangular Cartesian coordinate systems Oxy (Fig. 4) is taken to mean A(x;y) abo A = (x; y).
Respect. Point O, called cob of coordinates, maє coordinates O(0 ; 0) .
Business value 5. In rectangular Cartesian coordinate systems Oxy, the numerical weight Ox is called the abscis, and the numerical weight Oy is called the ordinate (Fig. 5).
Business value 6. The dermal rectangular Cartesian coordinate system extends the area into 4 parts (quadrant), the numbering of which is shown in little 5.
Business value 7. The area, given a rectangular Cartesian coordinate system, is called coordinate area.
Respect. The abscissa is set to the coordinate area y= 0, all the ordinates are set to the coordinate area x = 0.
Tverdzhennya 1. Show me two dots coordinate area
A 1 (x 1 ;y 1) і A 2 (x 2 ;y 2)
be counted for the formula
Delivered. Figure 6 is visible.
