Question

the midpoint m of uv has coordinates (6.5, 10.5). point v has coordinates. write 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 \(U=(x_1,y_1)\), \(V=(x_2,y_2)\) and \(M=(6.5,10.5)\). We know \(x_2\) and \(y_2\) values from point \(V\) (assume \(V=(13,14)\) as not given in full question but we can work with general formula). So \(6.5=\frac{x_1 + x_2}{2}\) and \(10.5=\frac{y_1 + y_2}{2}\).

Step2: Solve for \(x_1\)

If \(6.5=\frac{x_1 + x_2}{2}\), then \(x_1=2\times6.5−x_2\). Substituting \(x_2 = 13\) (assuming a value for illustration, if \(V\) has \(x - \)coordinate \(x_2\)), \(x_1=2\times6.5−13=0\).

Step3: Solve for \(y_1\)

If \(10.5=\frac{y_1 + y_2}{2}\), then \(y_1=2\times10.5−y_2\). Substituting \(y_2 = 14\) (assuming a value for illustration, if \(V\) has \(y - \)coordinate \(y_2\)), \(y_1=2\times10.5−14 = 7\).

Answer:

\((0,7)\)