Answer:
x = 7 and y = 1
Step-by-step explanation:
Coordinates of Coffee shop = (12, 16)
Coordinates of Library = (16, 8)
School has been shifted to the new position so that distance of school is preserved from the coffee shop.
Coordinates of the new position of school = (15, 10)
Ratio in which distance between coffee shop and library is divided by the location of school is x : y.
If a segment having extreme ends [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is divided into two parts by point (x, y) in the ratio of m : n,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
From the points given in the picture,
15 = [tex]\frac{16x+8y}{x+y}[/tex]
15x + 15y = 16x + 8y
15y - 8y = 16x - 15x
7y = x
[tex]\frac{x}{y}=\frac{7}{1}[/tex]
Therefore, x = 7 and y = 1 will be the answer.
