Find the Start Point Given Mid (1,-62) and End (-1,-3.4) (1,-62) , (-1,-3.4)

$(1, - 62)$ , $(- 1, - 3.4)$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

Simplify each term.

Multiply $2$ by $1$ .

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

Multiply $- 1$ by $- 1$ .

$x_{1} = 2 + 1$

Add $2$ and $1$ .

$x_{1} = 3$

Step 6

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

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

Step 7

Solve for $y_{1}$ .

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

Step 8

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

$y_{1} = 2 (- 62) - (- 3.4)$

Step 9

Simplify the right side of $y_{1} = 2 (- 62) - (- 3.4)$ .

Simplify each term.

Multiply $2$ by $- 62$ .

$y_{1} = - 124 - (- 3.4)$

Multiply $- 1$ by $- 3.4$ .

$y_{1} = - 124 + 3.4$

Add $- 124$ and $3.4$ .

$y_{1} = - 120.6$

Step 10

The start point is $(3, - 120.6)$ .

$(3, - 120.6)$