Answer:
B. At the corner of 10th Street and 17th Avenue.
Step-by-step explanation:
The point (x,y) which divides the segment AB with endpoints at [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex] in ratio [tex]m:n[/tex] has coordinates
[tex]x=\dfrac{nx_1+nx_2}{m+n}\\ \\y=\dfrac{ny_1+ny_2}{m+n}[/tex]
In your case,
[tex]T(4,8)[/tex]
[tex]L(12,20)[/tex]
The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then [tex]TM:TL=3:4[/tex] or [tex]TM:ML=3:1[/tex]
Thus,
[tex]x=\dfrac{1\cdot 4+3\cdot 12}{3+1}=\dfrac{4+36}{4}=\dfrac{40}{4}=10\\ \\y=\dfrac{1\cdot 8+3\cdot 20}{3+1}=\dfrac{8+60}{4}=\dfrac{68}{4}=17[/tex]
So, the fruit market is at point [tex]F(10,17)[/tex] which ,=means it is placed at the corner of 10th Street and 17th Avenue.
