Question

5 ab has endpoint ( a(-2,3) ) and midpoint ( m(4,6) ). find the coordinates ( (x,y) ) of ( b ).

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 \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Given \(A(-2,3)\) and \(M(4,6)\), let \(B=(x,y)\). Then \(\frac{-2 + x}{2}=4\) and \(\frac{3 + y}{2}=6\).

Step2: Solve for \(x\)

For \(\frac{-2 + x}{2}=4\), multiply both sides by \(2\): \(-2+x = 8\). Add \(2\) to both sides: \(x=8 + 2=10\).

Step3: Solve for \(y\)

For \(\frac{3 + y}{2}=6\), multiply both sides by \(2\): \(3 + y=12\). Subtract \(3\) from both sides: \(y=12-3 = 9\).

Answer:

\((10,9)\)