Question

the midpoint of ab is m(-1,6). if the coordinates of a are (-5,7), what are the coordinates of b?

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Given \(M(-1,6)\) and \(A(-5,7)\), let the coordinates of \(B\) be \((x,y)\).
For the x - coordinate: \(\frac{-5 + x}{2}=-1\).

Step2: Solve for x

Multiply both sides of \(\frac{-5 + x}{2}=-1\) by 2: \(-5 + x=-2\). Then add 5 to both sides: \(x=-2 + 5=3\).

Step3: Solve for y

For the y - coordinate, \(\frac{7 + y}{2}=6\). Multiply both sides by 2: \(7 + y = 12\). Subtract 7 from both sides: \(y=12 - 7 = 5\).

Answer:

\((3,5)\)