Question

the midpoint of the segment $overline{ab}$ is $(-3,1)$ and point a is located at $(-5,-4)$. what is location of point b?

a. $(-8,3)$
b. $(-1,6)$
c. $(-2,5)$
d. there is not enough informaiton for this to be determined.

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 \(A(-5,-4)\) and \(M(-3,1)\), and \(B(x,y)\). Then \(\frac{-5 + x}{2}=-3\) and \(\frac{-4 + y}{2}=1\).

Step2: Solve for \(x\)

From \(\frac{-5 + x}{2}=-3\), multiply both sides by \(2\): \(-5+x=-6\). Add \(5\) to both sides: \(x=-6 + 5=-1\).

Step3: Solve for \(y\)

From \(\frac{-4 + y}{2}=1\), multiply both sides by \(2\): \(-4 + y=2\). Add \(4\) to both sides: \(y=2+4 = 6\).

Answer:

B. \((-1,6)\)