Question

geometry
su_std gf unit 1a test a
name: jayson
date: 9/15/25 pd: 7
/73 = _ %
slope: $\frac{y_2 - y_1}{x_2 - x_1}$
midpoint formula: $x_{midpoint}=\frac{x_1 + x_2}{2}$, $y_{midpoint}=\frac{y_1 + y_2}{2}$
distance formula: $sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
show all work. include units where appropriate.
sketch each of the following. then name the figure using the correct notation. (2 pts. each)

1. angle abc

sketch
notation

1. segment cd

sketch
notation

1. line hg

sketch
notation

1. sketch opposite rays $overrightarrow{sy}$ and $overrightarrow{sp}$
2. point m is the midpoint of $overline{jk}$. solve for x and find the length of $overline{jk}$, when jm = x + 15 and mk is 4x - 45. draw a picture and show work. (3 pts.)

x = _
jk = _

1. point c is between w and m. if wm is 32 and wc is 18, what is cm? draw a picture and show work. (3 pts.)

cm = _

Explanation:

Step1: Angle ABC notation

∠ABC

Step2: Segment CD notation

$\overline{CD}$

Step3: Line HG notation

$\overleftrightarrow{HG}$

Step4: Opposite rays SY, SP notation

$\overrightarrow{SY}$ and $\overrightarrow{SP}$

Step5: Solve for x (midpoint)

$x + 15 = 4x - 45 \implies 3x = 60 \implies x = 20$

Step6: Calculate JK length

$JK = (20+15) + (4*20-45) = 70$

Step7: Calculate CM length

$CM = 32 - 18 = 14$

Answer:

∠ABC
$\overline{CD}$
$\overleftrightarrow{HG}$
$\overrightarrow{SY}$ and $\overrightarrow{SP}$
x=20
JK=70
CM=14