Answer:
18) Area= 5*5/2=25/2=12.5 unit ^2
19) Area=AB^2V3/4=8a^2*V3/4=2V3a^2
Explanation:
18. A(-3,0)
B(1,-3)
C(4,1)
AB=V(-3-1)^2+(0+3)^2=V16+9=V25=5
AC=V(-3-4)^2+(0-1)^2=V49+1=V50=5V2
BC=V(1-4)^2+(-3-1)^2=V9+16=V25=5
so AB=BC=5
and AC^2=AB^2+BC^2
so trg ABC is an isosceles right angle triangle (<B=90)
Area= 5*5/2=25/2=12.5 unit ^2
19. A(a,a)
B(-a,-a)
C(-V3a, V3a)
AB=V(a+a)^2+(a+a)^2=V4a^2+4a^2=V8a^2
AC=V(a+V3a)^2+(a-V3)^2=Va^2+2a^2V3+3a^2+a^2-2a^2V3+3a^2=V8a^2
BC=V(-a+V3a)^2+(-a-V3a)^2=V8a^2
so AB=AC=BC
Area=AB^2V3/4=8a^2*V3/4=2V3a^2