Question

the midpoint of pq is m(5, 4). one endpoint is q(10, 0). find the coordinates of the other endpoint p. write the coordinates as decimals or integers. p = ( )

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 \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Let \(P=(x,y)\), \(Q=(10,0)\) and \(M=(5,4)\).

Step2: Find the x - coordinate of \(P\)

We know that \(\frac{x + 10}{2}=5\). Multiply both sides by 2: \(x + 10=10\). Then subtract 10 from both sides: \(x=0\).

Step3: Find the y - coordinate of \(P\)

We know that \(\frac{y + 0}{2}=4\). Multiply both sides by 2: \(y+0 = 8\), so \(y = 8\).

Answer:

\((0,8)\)