Find the Start Point Given Mid (18.6,-1) and End (1,-34) (18.6,-1) , (1,-34)

$(18.6, - 1)$ , $(1, - 34)$

The midpoint formula is $M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ .

$M = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Set the $x_{M}$ equal to the $x_{M}$ coordinate.

$x_{M} = \frac{x_{1} + x_{2}}{2}$

Solve for $x_{1}$ to get $x_{1} = 2 x_{M} - x_{2}$ .

$x_{1} = 2 x_{M} - x_{2}$

Substitute the values for $x_{M}$ and $x_{2}$ in $x_{1} = 2 x_{M} - x_{2}$ .

$x_{1} = 2 (18.6) - (1)$

Simplify the right side of $x_{1} = 2 (18.6) - (1)$ .

Simplify each term.

Multiply $2$ by $18.6$ .

$x_{1} = 37.2 - (1)$

Multiply $- 1$ by $1$ .

$x_{1} = 37.2 - 1$

Subtract $1$ from $37.2$ .

$x_{1} = 36.2$

Set the $y_{M}$ equal to the $y_{M}$ coordinate.

$y_{M} = \frac{y_{1} + y_{M}}{2}$

Solve for $y_{1}$ .

$y_{1} = 2 y_{M} - y_{2}$

Substitute the values for $y_{M}$ and $y_{2}$ in $y_{1} = 2 y_{M} - y_{2}$ .

$y_{1} = 2 (- 1) - (- 34)$

Simplify the right side of $y_{1} = 2 (- 1) - (- 34)$ .

Simplify each term.

Multiply $2$ by $- 1$ .

$y_{1} = - 2 - (- 34)$

Multiply $- 1$ by $- 34$ .

$y_{1} = - 2 + 34$

Add $- 2$ and $34$ .

$y_{1} = 32$

The start point is $(36.2, 32)$ .

$(36.2, 32)$