You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
ÿêèé íàðîäèâñÿ â ëþòîìó. Ïàðàìåòð ì äîð³âíþº 2. Êîîðäèíàòè<br />
âåðøèí òðèêóòíèêà áóäóòü òàê³: À (–2, 4), Â (6, –2),<br />
Ñ (8, 7).<br />
Ðîçâ’ÿçàííÿ. 1) ³äñòàíü ì³æ äâîìà òî÷êàìè âèçíà-<br />
÷èìî çà äîïîìîãîþ ôîðìóëè (4.1.3 ). Çàñòîñîâóþ÷è ¿¿, çíàéäåìî<br />
äîâæèíó ñòîð³í À ³ ÀÑ:<br />
2 2 2<br />
2<br />
AB = ( 6-( - 2)<br />
) + (-2- 4) = 8 + (- 6)<br />
= 100 = 10 .<br />
2 2<br />
AC = ( 8+ 2) + ( 7- 4)<br />
= 109 .<br />
2) Ó â³äïîâ³äíîñò³ äî ï. 4.3.4 ð³âíÿííÿ ïðÿìî¿, ÿêà ïðîõîäèòü<br />
÷åðåç òî÷êè À ³ Â, òàêå:<br />
y- 4 x+<br />
2<br />
=<br />
-2- 4 6+ 2<br />
.<br />
Çâ³äêè 3õ +4ó − 10 = 0 (ÀÂ). Ùîá çíàéòè êóòîâèé êîåô³ö³ºíò<br />
k AB ïðÿìî¿ ÀÂ, ðîçâ’ÿæåìî îòðèìàíå ð³âíÿííÿ â³äíîñíî<br />
ó:<br />
ó = −3/4õ + 5/2, òàêèì ÷èíîì k AB = −3/4.<br />
Àíàëîã³÷íî çíàéäåìî ð³âíÿííÿ ïðÿìî¿ ÀÑ:<br />
3õ − 10ó + 46 = 0 ³ ïðÿìî¿ ÂÑ: 9x − 2y − 58 = 0. Êóòîâ³ êîåô³ö³ºíòè<br />
ïðÿìèõ ÀÑ ³ ÂÑ òàê³: k AÑ = 3/10, k ÂÑ =9/2.<br />
3) Âíóòð³øí³é êóò ïðè âåðøèí³ À ïîçíà÷èìî ÷åðåç α.<br />
42<br />
Òîä³, çàñòîñîâóþ÷è ôîðìóëó (4.3.8), çíàéäåìî, ùî tga= .<br />
31<br />
42<br />
Îòæå, øóêàíèé êóò a= arctg . 31<br />
4) Íåõàé D — ñåðåäèíà â³äð³çêó ÂÑ. Äëÿ âèçíà÷åííÿ<br />
êîîðäèíàò òî÷êè D çàñòîñóºìî ôîðìóëè (4.1.7) ä³ëåííÿ â³äð³çêà<br />
ïîïîëàì:<br />
6+ 8 - 2+<br />
7 5<br />
xD<br />
= = 7, yD<br />
= = .<br />
2 2 2<br />
Äàë³, çàñòîñîâóþ÷è ôîðìóëó (4.3.19) (ð³âíÿííÿ ïðÿìî¿,<br />
ÿêà ïðîõîäèòü ÷åðåç äâ³ òî÷êè), îòðèìàºìî ð³âíÿííÿ ìåä³àíè<br />
ÀD:<br />
y- 4 x+<br />
2<br />
= Þ x+ 6× y- 22 = 0 ( AD)<br />
.<br />
5 7+<br />
2<br />
- 4<br />
2<br />
5) Âèñîòà CP ïåðïåíäèêóëÿðíà ñòîðîí³ A (P — òî÷êà<br />
ïåðåòèíó ïåðïåíäèêóëÿðà ³ ñòîðîíè ÀÂ). Òîìó çà êðèòåð³-<br />
ºì ïåðïåíäèêóëÿðíîñò³ äâîõ ïðÿìèõ (äèâ. ï. 4.3.2) ¿õí³<br />
êóòîâ³ êîåô³ö³ºíòè ïîâ’ÿçàí³ ð³âí³ñòþ k CP = −1/k AB . Îñê³ëüêè<br />
ìè çíàéøëè ðàí³øå, ùî k AB = −3/4, òî k CP = 4/3. Çíàþ÷è<br />
êîîðäèíàòè òî÷êè Ñ (8, 7) ³ êóòîâèé êîåô³ö³ºíò k AB , çà ôîðìóëîþ<br />
(4.3.13) ñêëàäåìî ð³âíÿííÿ âèñîòè ÑÐ:<br />
ó − 7 = 4/3 (õ − 8) ⇒ 4õ − 3ó − 11 = 0 (ÑÐ).<br />
6) Ç êóðñó ìàòåìàòèêè ñåðåäíüî¿ øêîëè â³äîìî, ùî á³ñåêòðèñà<br />
êóòà òðèêóòíèêà ÀÂÑ ïðè âåðøèí³ À ìຠâëàñòèâ³ñòü<br />
AB BK<br />
= .<br />
AC KC<br />
Çã³äíî ç ðåçóëüòàòàìè ðîçâ’ÿçêó 1) ìàòèìåìî<br />
BK<br />
λ= =<br />
KC<br />
10 .<br />
109<br />
Òåïåð, çíàþ÷è êîîðäèíàòè òî÷îê  ³ Ñ, çà ôîðìóëàìè<br />
(4.1.6) çíàéäåìî êîîðäèíàòè òî÷êè L (îñíîâè á³ñåêòðèñè,<br />
ïðîâåäåíî¿ ç âåðøèíè À):<br />
80 + 6 109 70 -2 109<br />
xL<br />
= , yL<br />
=<br />
.<br />
10 + 109 10 + 109<br />
Ó â³äïîâ³äíîñò³ äî ôîðìóëè (4.3.18) îòðèìàºìî ð³âíÿííÿ<br />
á³ñåêòðèñè AL:<br />
30 - 6 109<br />
y- 4 = ( x+<br />
2 )( AL)<br />
.<br />
100 + 8 109<br />
120 121
Change language