Question

vw has a midpoint at m(6, 4). point w is at (5, 3). find the coordinates of point v. write the coordinates as decimals or integers. v = (□, □)

Explanation:

Step1: Recall the mid - point formula

The mid - point formula for two points \(V(x_1,y_1)\) and \(W(x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Let \(V=(x,y)\), \(W=(5,3)\) and \(M=(6,4)\).

Step2: Solve for \(x\)

We know that \(\frac{x + 5}{2}=6\).
Multiply both sides by \(2\): \(x + 5=12\).
Subtract \(5\) from both sides: \(x=12 - 5=7\).

Step3: Solve for \(y\)

We know that \(\frac{y + 3}{2}=4\).
Multiply both sides by \(2\): \(y + 3=8\).
Subtract \(3\) from both sides: \(y=8 - 3=5\).

Answer:

\((7,5)\)