Question

name bisectors - practice suppose m is the mid - point of (overline{fg}), find the value of the variable. show all work used to arrive at your answers. use a diagram if necessary. 1. (fm = 5y+13), (mg = 5 - 3y) 2. (fm = 3x - 4), (mg = 5x - 26) 3. (fm = 3n + 1), (mg = 6 - 2n) 4. (fm = 12x - 4), (mg = 5x + 10) 5. (fm = 2k - 5), (fg = 18), (k=)? 6. find the value of y if m is the mid - point of (overline{ln}).

Explanation:

1.

Step1: Set FM equal to MG since M is the mid - point

$5y + 13=5 - 3y$

Step2: Add 3y to both sides

$5y+3y + 13=5-3y + 3y$
$8y+13 = 5$

Step3: Subtract 13 from both sides

$8y+13-13=5 - 13$
$8y=-8$

Step4: Divide both sides by 8

$y=\frac{-8}{8}=-1$

Step1: Set FM equal to MG since M is the mid - point

$3x-4 = 5x-26$

Step2: Subtract 3x from both sides

$3x-3x-4=5x-3x - 26$
$-4 = 2x-26$

Step3: Add 26 to both sides

$-4 + 26=2x-26 + 26$
$22=2x$

Step4: Divide both sides by 2

$x=\frac{22}{2}=11$

Step1: Set FM equal to MG since M is the mid - point

$3n + 1=6-2n$

Step2: Add 2n to both sides

$3n+2n + 1=6-2n+2n$
$5n + 1=6$

Step3: Subtract 1 from both sides

$5n+1 - 1=6 - 1$
$5n=5$

Step4: Divide both sides by 5

$n=\frac{5}{5}=1$

Answer:

$y = - 1$

2.