Question

1. midpoint of pq is (4,3) and p is (7,8). what are the coordinates of q?

Explanation:

Step1: Recall the midpoint formula

The midpoint 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 \(M=(4,3)\), \(P=(7,8)\) and \(Q=(x,y)\).

Step2: Set up equations for \(x\) and \(y\) coordinates

For the \(x\) - coordinate: \(\frac{7 + x}{2}=4\). Multiply both sides by 2: \(7 + x = 8\). Then \(x=8 - 7=1\).
For the \(y\) - coordinate: \(\frac{8 + y}{2}=3\). Multiply both sides by 2: \(8 + y = 6\). Then \(y=6 - 8=-2\).

Answer:

The coordinates of \(Q\) are \((1,-2)\)