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
submit answer
© watch video
show ex

Explanation:

Step1: Use the 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 \(M=(-3,-2)\). For the \(x\) - coordinate: \(\frac{1 + x_2}{2}=-3\).

Step2: Solve for \(x\) - coordinate of \(B\)

Multiply both sides of \(\frac{1 + x_2}{2}=-3\) by \(2\): \(1 + x_2=-6\). Then subtract \(1\) from both sides: \(x_2=-6 - 1=-7\).

Step3: Solve for \(y\) - coordinate of \(B\)

For the \(y\) - coordinate, use \(\frac{-7 + y_2}{2}=-2\). Multiply both sides by \(2\): \(-7 + y_2=-4\). Then add \(7\) to both sides: \(y_2=-4 + 7 = 3\).

Answer:

The coordinates of \(B\) are \((-7,3)\)