Answer:
[tex]A(-\frac{20}{3} ,-\frac{13}{3})[/tex]
Step-by-step explanation:
Point B partitions AC in a 3:4 ratio.
B is located at (4,1) and C is located at (12,5).
Let [tex](x_1,y_1)[/tex] be the coordinates of A.
Then [tex](\frac{mx_1+nx_2}{m+n}, \frac{my_1+ny_2}{m+n})=(4,1)[/tex]
But m:n=3:4 implies m=3 and n=4 and [tex](x_2=12,y_2=5)[/tex]
[tex](\frac{3x_1+4*12}{3+4}, \frac{3y_1+4*5}{3+4})=(4,1)[/tex]
[tex](\frac{3x_1+48}{7}, \frac{3y_1+20}{7})=(4,1)[/tex]
[tex]\frac{3x_1+48}{7}=4, \frac{3y_1+20}{7}=1[/tex]
[tex]3x_1+48=28, 3y_1+20=7[/tex]
[tex]3x_1=-20, 3y_1=-13[/tex]
[tex]x_1=-\frac{20}{3} , y_1=-\frac{13}{3}[/tex]
