Question

geo lesson 2.2 homework
name beatriz marcos

1. use the figure to answer the parts.

a c d e f g h b
a. what is the mid - point of line segment cg?
b. is the mid - point of ab currently labeled on the figure?
c. name two different line segments for which point d is the mid - point.

1. point x is located at (7, - 4) and point y is located at (-5,4).

a. draw xy on the grid provided.
b. plot the mid - point of xy and label it as point z.
c. what are the coordinates of the mid - point?

1. point m is located at (24,17) and point n is located at (3, - 4). find the mid - point of line segment mn.
2. the mid - point of line segment st is (-4, - 5). if point s is located at (-4, - 12), what is the location of point t?

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Solve 1a

For the line segment $CG$, assume each point is evenly spaced. $C$ and $G$ have 4 points between them. The mid - point is $E$.

Step3: Solve 2c

For points $X(7,-4)$ and $Y(-5,4)$, using the mid - point formula:
$x=\frac{7+( - 5)}{2}=\frac{7 - 5}{2}=1$
$y=\frac{-4 + 4}{2}=0$
The mid - point coordinates are $(1,0)$.

Step4: Solve 3

For points $M(24,17)$ and $N(3,-4)$:
$x=\frac{24 + 3}{2}=\frac{27}{2}=13.5$
$y=\frac{17+( - 4)}{2}=\frac{17 - 4}{2}=\frac{13}{2}=6.5$
The mid - point of $MN$ is $(13.5,6.5)$.

Step5: Solve 4

Let the coordinates of $T$ be $(x,y)$. Given the mid - point of $ST$ is $(-4,-5)$ and $S(-4,-12)$.
For the $x$ - coordinate: $\frac{-4 + x}{2}=-4$, then $-4+x=-8$, so $x=-4$.
For the $y$ - coordinate: $\frac{-12 + y}{2}=-5$, then $-12 + y=-10$, so $y = 2$.
The location of point $T$ is $(-4,2)$.

Answer:

1a. $E$
2c. $(1,0)$

1. $(13.5,6.5)$
2. $(-4,2)$