Question

the midpoint m of $overline{uv}$ has coordinates (0.5, -2.5). point v has coordinates (-18, 0). find the coordinates of point u. write the coordinates as decimals or integers. u = ( )

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $U(x_1,y_1)$ and $V(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. We know $M(0.5,-2.5)$ and $V(-18,0)$.

Step2: Solve for $x$ - coordinate of $U$

Set up the equation for the $x$ - coordinate of the mid - point: $\frac{x_1+( - 18)}{2}=0.5$. Multiply both sides by 2: $x_1-18 = 1$. Then add 18 to both sides: $x_1=1 + 18=19$.

Step3: Solve for $y$ - coordinate of $U$

Set up the equation for the $y$ - coordinate of the mid - point: $\frac{y_1 + 0}{2}=-2.5$. Multiply both sides by 2: $y_1=-5$.

Answer:

$(19,-5)$