Question

the midpoint m of $overline{uv}$ has coordinates (64.5, -46.5). point v has coordinates (66, -29). 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 \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Let \(U=(x,y)\) and \(V=(66,-29)\), and \(M=(64.5,-46.5)\).

Step2: Solve for \(x\) - coordinate of \(U\)

We know that \(\frac{x + 66}{2}=64.5\). Multiply both sides by 2: \(x + 66=129\). Then subtract 66 from both sides: \(x=129 - 66=63\).

Step3: Solve for \(y\) - coordinate of \(U\)

We know that \(\frac{y+( - 29)}{2}=-46.5\). Multiply both sides by 2: \(y-29=-93\). Then add 29 to both sides: \(y=-93 + 29=-64\).

Answer:

\((63,-64)\)