Question

question
the midpoint of ab is m(-3,-2). if the coordinates of a are (1,-7), what are the coordinates of b?
answer attempt 1 out of 2
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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 \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Let \(A=(1,-7)\) and \(B=(x,y)\), and \(M=(-3,-2)\).

Step2: Solve for \(x\)

For the \(x\) - coordinate: \(\frac{1 + x}{2}=-3\). Multiply both sides by \(2\): \(1 + x=-6\). Then \(x=-6 - 1=-7\).

Step3: Solve for \(y\)

For the \(y\) - coordinate: \(\frac{-7 + y}{2}=-2\). Multiply both sides by \(2\): \(-7 + y=-4\). Then \(y=-4 + 7 = 3\).

Answer:

\((-7,3)\)