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

The coordinates of the library are (19,20)

Step-by-step 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

Let

M ---> the cafeteria

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

(x2,y2) ----> library

substitute the given values

so

therefore

The coordinates of the library are (19,20)

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

step-by-step explanation: