Question

s is the midpoint of rt. r has coordinates (3, -3), and s has coordinates (-5, 5). find the coordinates of t.

Explanation:

Step1: Use the mid - point formula

The mid - point formula for two points \(R(x_1,y_1)\) and \(T(x_2,y_2)\) is \(S(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Given \(R(3,-3)\) and \(S(-5,5)\), let \(T=(x,y)\).
For the \(x\) - coordinate: \(\frac{3 + x}{2}=-5\).

Step2: Solve for \(x\)

Multiply both sides of \(\frac{3 + x}{2}=-5\) by \(2\): \(3 + x=-10\). Then subtract \(3\) from both sides: \(x=-10 - 3=-13\).

Step3: Solve for \(y\)

For the \(y\) - coordinate: \(\frac{-3 + y}{2}=5\). Multiply both sides by \(2\): \(-3 + y = 10\). Then add \(3\) to both sides: \(y=10 + 3 = 13\).

Answer:

\((-13,13)\)