Question

At peninsula high school the cafeteria is collinear and equidistant from the science building and the library the science building is located (5,12) on a coordinate plan and the cafeteria is at (12,16) find the coordinates of the library

Answer 1

The coordinates of the library are (19,20)

Explanation:

we know that

If the cafeteria is collinear and equidistant from the science building and the library

then

the cafeteria is the midpoint between the science building and the library

The formula to calculate the midpoint between two points is

`M=((x1+x2)/(2),(y1+y2)/(2))`

Let

M ---> the cafeteria

(x1,y1) ----> science building

(x2,y2) ----> library

substitute the given values

`(12,16)=((5+x2)/(2),(12+y2)/(2))`

so

`12=(5+x2)/2\\24=5+x2\\x2=24-5=19`

`16=(12+y2)/2\\32=12+y2\\y2=32-12=20`

therefore

The coordinates of the library are (19,20)