Question

Mrs. Williams' desk is located at (-5,2). The wireless internet box is halfway between her desk and the door. If the box is located at the coordinates (8, -8), what are the coordinates of the door?

Answer 1

Let that be (x,y)

So

`\\ \rm\rightarrowtail (8,-8)=((x-5)/(2),(y+2)/(2))`

`\\ \rm\rightarrowtail \cfrac{x-5}{2}=8\implies x-5=16\implies x=21`

`\\ \rm\rightarrowtail \cfrac{y+2}{2}=-8\implies y+2=-16\implies y=-18`

• (x,y)=(21,-18)

Answer 2

Topic : Midpoint between points

• desk = (-5,2)

• box = (8, -8)

• door = (x, y)

formula:

`\sf \bold{(x_m, y_m) = ((x_1+x_2)/(2), (y_1+y_2)/(2))}`

=====================================

`\hookrightarrow \sf (x+(-5))/(2) ,(y+2)/(2) = (8, -8)`

separate taking coefficients:

`\rightarrow \sf (x-5)/(2) =8, \ (y+2)/(2) = -8`

`\rightarrow \sf x-5 =16, \ y+2 = -16`

`\rightarrow \sf x =16+5, \ y= -16-2`

`\rightarrow \sf x =21, \ y= -18`

coordinates of door: (21, -18)