Question

question 4
1 pts

1. the midpoint of $overline{xz}$ is $y$. which of the following is true?

f $xz = xy$
g $xz=\frac{1}{2}xy$
h $yz=\frac{1}{2}xy$
i $yz=\frac{1}{2}xz$

question 5
1 pts
use the graph at the right for exercises 5 and 6.

1. according to the graph, what is the mid - point of $overline{ab}$?

a $(1,0)$
b $(1, - 0.5)$
c $(1,0.5)$
d $(1.5,-0.5)$

Explanation:

Step1: Recall mid - point definition

A mid - point divides a line segment into two equal parts. If $Y$ is the mid - point of $\overline{XZ}$, then $XY = YZ$ and $YZ=\frac{1}{2}XZ$ and $XY=\frac{1}{2}XZ$.

Step1: Identify coordinates of endpoints

Let's assume $A(x_1,y_1)$ and $B(x_2,y_2)$. From the graph, if we assume $A(0, - 1)$ and $B(2,1)$.

Step2: Use mid - point formula

The mid - point formula is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Substitute $x_1 = 0,x_2=2,y_1=-1,y_2 = 1$ into the formula: $\frac{0 + 2}{2}=1$ and $\frac{-1 + 1}{2}=0$. The mid - point is $(1,0)$.

Answer:

I. $YZ=\frac{1}{2}XZ$