Question

the midpoint m of qr has coordinates (8, 7). point r has coordinates (10, 4). find the coordinates of point q. write the coordinates as decimals or integers. q = ( )

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points \(Q(x_1,y_1)\) and \(R(x_2,y_2)\) is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). We know \(M(8,7)\) and \(R(10,4)\), let \(Q=(x,y)\).

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

We have \(\frac{x + 10}{2}=8\). Multiply both sides by 2: \(x + 10=16\). Then subtract 10 from both sides: \(x=16 - 10=6\).

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

We have \(\frac{y + 4}{2}=7\). Multiply both sides by 2: \(y + 4=14\). Then subtract 4 from both sides: \(y=14 - 4 = 10\).

Answer:

\((6,10)\)