Question

the midpoint of \\( \overline { a b } \\) is \\( m ( - 4, - 5 ) \\). if the coordinates of \\( a \\) are \\( ( - 7, - 8 ) \\), what are the coordinates of \\( b \\)?
answer
attempt 1 out of 2

Explanation:

Step1: Use 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 \(M(-4,-5)\) and \(A(-7,-8)\), let \(B=(x,y)\).
For the \(x\) - coordinate: \(\frac{-7 + x}{2}=-4\).

Step2: Solve for \(x\)

Multiply both sides of \(\frac{-7 + x}{2}=-4\) by \(2\): \(-7+x=-8\). Then add \(7\) to both sides: \(x=-8 + 7=-1\).
For the \(y\) - coordinate: \(\frac{-8 + y}{2}=-5\).

Step3: Solve for \(y\)

Multiply both sides of \(\frac{-8 + y}{2}=-5\) by \(2\): \(-8 + y=-10\). Then add \(8\) to both sides: \(y=-10 + 8=-2\).

Answer:

\((-1,-2)\)