Question

question 2 of 10
one of the endpoints of line segment ab is b(-16,-3). determine the coordinates of point a if the midpoint of the segment is m(-6,-8).

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 \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Let \(A=(x,y)\), \(B=(-16,-3)\) and \(M=(-6,-8)\).

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

We know that \(\frac{x+( - 16)}{2}=-6\). Multiply both sides by 2: \(x - 16=-12\). Then add 16 to both sides: \(x=-12 + 16=4\).

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

We know that \(\frac{y+( - 3)}{2}=-8\). Multiply both sides by 2: \(y-3=-16\). Then add 3 to both sides: \(y=-16 + 3=-13\).

Answer:

\((4,-13)\)