Question

the point y is the mid - point of $overline{xz}$. find the location of z.
location of z :

Explanation:

Step1: Recall mid - point formula

The mid - point formula for a one - dimensional number line is $Y=\frac{X + Z}{2}$, where $Y$ is the mid - point of the line segment with endpoints $X$ and $Z$.

Step2: Rearrange the formula to solve for $Z$

Starting from $Y=\frac{X + Z}{2}$, we multiply both sides by 2 to get $2Y=X + Z$. Then we subtract $X$ from both sides, so $Z = 2Y−X$.

Step3: Substitute the given values of $X$ and $Y$

We know that $X=-2$ and $Y = 6$. Substituting these values into the formula $Z = 2Y−X$, we have $Z=2\times6-(-2)$.

Step4: Calculate the value of $Z$

First, $2\times6 = 12$, and $-(-2)=2$. Then $Z=12 + 2=14$.

Answer:

14