Question

question the midpoint of ab is m(0, - 3). if the coordinates of a are (1, 2), what are the coordinates of b? answer attempt 1 out of 2 submit answer watch video show examples

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 \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Here \(x_1 = 1,y_1=2\) and \(M=(0,-3)\).

Step2: Solve for \(x_2\)

We have \(\frac{x_1 + x_2}{2}=0\), substituting \(x_1 = 1\) into it: \(\frac{1 + x_2}{2}=0\), then \(1+x_2=0\times2 = 0\), so \(x_2=-1\).

Step3: Solve for \(y_2\)

We have \(\frac{y_1 + y_2}{2}=-3\), substituting \(y_1 = 2\) into it: \(\frac{2 + y_2}{2}=-3\), then \(2 + y_2=-3\times2=-6\), so \(y_2=-6 - 2=-8\).

Answer:

\((-1,-8)\)