Question

the mid - point of pq is m=(2,0). one endpoint is p=(8,7). find the coordinates of the other endpoint, q.

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points \(P(x_1,y_1)\) and \(Q(x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Given \(M=(2,0)\), \(P=(8,7)\), let \(Q=(x,y)\).

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

We have \(\frac{8 + x}{2}=2\). Cross - multiply: \(8 + x=4\). Then \(x=4 - 8=-4\).

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

We have \(\frac{7 + y}{2}=0\). Cross - multiply: \(7 + y=0\). Then \(y=-7\).

Answer:

\(Q=(-4,-7)\)