Question

M is the midpoint of CD. C is located at (-2,12) and D is located at (4,6). If g is a two digit number that has the x coordinate of M as it's tens digit and the y coordinate of M as its ones digit, what is the value of g?

Answer 1

If we know that
`x = 1` and
`y = 9`, the value of
`g` is 19.

Explanation:

Let
`C(x,y) =(-2,12)` and
`D(x,y) =(4,6)`, from Analytical Geometry and Linear Algebra we have that midpoint of CD is determined by:

`M(x,y) = (1)/(2)\cdot C(x,y)+(1)/(2)\cdot D(x,y)` (Eq. 1)

`M(x,y) = (1)/(2)\cdot (-2,12)+(1)/(2)\cdot (4,6)`

`M(x,y) = (-1,6)+(2,3)`

`M(x,y) =(-1+2,6+3)`

`M(x,y)= (1,9)`

If we know that
`x = 1` and
`y = 9`, the value of
`g` is 19.