Question

ajutati maaaaa ex 3. si 4....​

Answer 1

4. Daca B este simetricul lui A fata de M, inseamna ca M este mijlocul lui AB

Deci M va avea coordonatele:

$M(\frac{x_B+x_A}{2}, \frac{y_B+y_A}{2})=M(1,4)\\\\x_B+x_A=2\\\\-2a+9-11=2\\\\-2a=4\\\\a=-2\\\\y_B+y_A=8\\\\2a+5+7=8\\\\2a=-4\\\\a=-2$

3.

$MN=\sqrt{(-1-4)^2+(3+9)^2} =\sqrt{25+144} =13\\\\MP=\sqrt{(8-4)^2+(-9+9)^2} =\sqrt{16}=4\\\\ NP=\sqrt{(8+1)^2+(-9-3)^2}=\sqrt{81+144}=\sqrt{225}=15$

$A_{MNP}=\sqrt{p(p-a)(p-b)(p-c)}$

Unde p este semiperimetru

a,b,c sunt laturile MN,MP,NP

$A_{MNP}=\sqrt{p(p-MN)(p-MP)(p-NP)}\\\\p=\frac{13+4+15}{2}=16\\\\ A_{MNP}=\sqrt{16(16-13)(16-4)(16-5)}=\sqrt{16\times3\times12\times1} =4\times6=24cm^2$