Question

: Consider the distance from the school to the coffee shop and the

distance from the library to the coffee shop. Draw their respective
line segments in the above graph. If the school is relocated in a
way that it is collinear to the coffee shop and the library, and the
distance to the coffee shop is preserved, then the point
representing the school will partition the line segment from the
coffee shop to the library in a x: y ratio. What are the values of x
and y?

Answer 1

x = 7 and y = 1

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
`(x_1,y_1)` and
`(x_2,y_2)` is divided into two parts by point (x, y) in the ratio of m : n,

x =
`(mx_2+nx_1)/(m+n)`

y =
`(my_2+ny_1)/(m+n)`

From the points given in the picture,

15 =
`(16x+8y)/(x+y)`

15x + 15y = 16x + 8y

15y - 8y = 16x - 15x

7y = x

`(x)/(y)=(7)/(1)`

Therefore, x = 7 and y = 1 will be the answer.