Question

the midpoint of ab is m(0, -7). if the coordinates of a are (2, -6), what are the coordinates of b? answer attempt 1 out of 2

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 \(x_1 = 2,y_1=-6\), and the mid - point \(M(0,-7)\).

Step2: Find the x - coordinate of B

We know that \(\frac{x_1 + x_2}{2}=0\), substituting \(x_1 = 2\) into it: \(\frac{2 + x_2}{2}=0\). Multiply both sides by 2: \(2+x_2 = 0\), then \(x_2=-2\).

Step3: Find the y - coordinate of B

We know that \(\frac{y_1 + y_2}{2}=-7\), substituting \(y_1=-6\) into it: \(\frac{-6 + y_2}{2}=-7\). Multiply both sides by 2: \(-6 + y_2=-14\). Add 6 to both sides: \(y_2=-8\).

Answer:

\((-2,-8)\)