Matematika ma’ruza-2

Mavzuga doir namunaviy masalaning yechimi

1-misol.Uchlari A(-7;4) , B(5;-5) va C(3;9) nuqtalarda bo‘lgan uchburchakni

1) AB tomon uzunligini;

2) AB tomon tenglamasini;

3) C uchidan AB tomonga tushirilgan CD balandlik tenglamasini;

4) CD balandlik uzunligini;

5) S uchburchak yuzini topib, shaklini chizing.

A (-7; 4)

С(3;9)

B(5;-5)

y

0 5

х

E(4;2)

D

Yechish: 1) ABtomon uzunligini (1) formulaga asosan,

2) AB tomon tenglamasini 1) formulaga ko‘ra:

Oxirgi tenglamani у ga nisbatan yechib, uchburchakni AB tomonini burchak koeffisentli tenglamasiga ega bo‘lamiz: -4y+16=3x+21, 3x+4y+5=0, 4y=-3x-5,

y=-(3/4)x-5/4, k=-3/4, b=-5/4=-1,25.

3) CD balandlik AB tomonga perpendikulyarligidan, uning burchak koeffisienti k=4/3 bo‘ladi.

Endi 4) formulaga asosan C(3;9) va k=4/3 ga ko‘ra

CD balandlik tenglamasini hosil qilamiz:

6) formulaga asosan C(3;9), nuqtadan x0=3,. у0=9 3x+4у+5=0 to’g’ri chiziqqacha bo’lgan masofa A=3, B=4, C=5, yani CD=d balandlikning uzunligi:

d=(3*3+4*9+5)/5= 50/5= 10 birlik, d=10.

4). BC tomon o‘rtasini koordinatasi E(x;у)

yuqorida keltirilgan formulaga asosan:

d=

E (4; 2) , AE-medianasi uzunligi ikki nuqta orasidagi masofani topish formulasia asosan, taqriban:

AE= 11,2 birlik ekan.

5) Uchburcak uchlarining A(-7;4) , B(5;-5) va C(3;9) koordinatalarini yuqorida keltirilgan uchburchakning yuzasini hisoblash formulalaridan biriga qo’yib hisoblaymiz:

S= ½( 45+35+12-20+15+63) = 75 kv.birlik