Question

71 given the number line below, what coordinate would you place point z at so that w is the mid - point of vz.

Explanation:

Step1: Identify coordinates of V and W

Let the coordinate of $V=-9$ and the coordinate of $W = - 6$.

Step2: Use mid - point formula

The mid - point formula on a number line is $W=\frac{V + Z}{2}$, where $W$ is the mid - point of the line segment with endpoints $V$ and $Z$.
We know $W=-6$ and $V = - 9$. Substitute into the formula: $-6=\frac{-9 + Z}{2}$.

Step3: Solve for Z

Multiply both sides of the equation by 2: $-6\times2=-9 + Z$.
So, $-12=-9 + Z$.
Add 9 to both sides: $Z=-12 + 9$.
$Z=-3$.

Answer:

$-3$