Question

geo lesson 2.2 homework

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:

1.

a.

Step1: Count segments between C and G

There are 4 equal - length segments between C and G. The mid - point is the 2nd point after C, which is E.

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $x_1=7,y_1 = - 4,x_2=-5,y_2 = 4$.

Step2: Calculate x - coordinate of mid - point

$x=\frac{7+( - 5)}{2}=\frac{7 - 5}{2}=1$

Step3: Calculate y - coordinate of mid - point

$y=\frac{-4 + 4}{2}=0$

Step1: Apply mid - point formula

For points $M(24,17)$ and $N(3,-4)$, use the mid - point formula $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$, where $x_1 = 24,y_1=17,x_2 = 3,y_2=-4$.

Step2: Calculate x - coordinate of mid - point

$x=\frac{24 + 3}{2}=\frac{27}{2}=13.5$

Step3: Calculate y - coordinate of mid - point

$y=\frac{17+( - 4)}{2}=\frac{17 - 4}{2}=\frac{13}{2}=6.5$

Answer:

E

b.