Question

1. find the coordinates of r if q(-1, 3) is the mid - point of pr and p has coordinates of (5, 6). guided practice 9. using the diagram to the left, find x, then qr. 10. if p is the mid - point of xy, xp = 8x - 2, and py = 12x - 30, find the value of x. 11. if g is the mid - point of fh, fg = 14x + 25, and gh = 73 - 2x, find fh.

Explanation:

Step1: Use mid - point formula

Let \(P(x_1,y_1)=(5,6)\) and \(Q(x_m,y_m)=(-1,3)\), and \(R(x_2,y_2)\). Mid - point formula: \(x_m=\frac{x_1 + x_2}{2}\), \(y_m=\frac{y_1 + y_2}{2}\).
For \(x\) - coordinate: \(-1=\frac{5 + x_2}{2}\), then \(-2 = 5+x_2\), \(x_2=-7\).
For \(y\) - coordinate: \(3=\frac{6 + y_2}{2}\), then \(6 = 6+y_2\), \(y_2 = 0\).

Step2: Find coordinates of \(R\)

\(R(-7,0)\)

Answer:

\(R(-7,0)\)