Question

square tuvw on the coordinate plane has points t (0, 0), u (5, 5), and v (0, 10). what are the coordinates of point w? a (5, - 5) b (5, 5) c (10, 5) d (10, 0)

Explanation:

Step1: Recall property of square

In a square, the mid - points of the diagonals coincide. Let the coordinates of \(T(0,0)\), \(U(5,5)\), \(V(0,10)\) and \(W(x,y)\). The mid - point formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). The diagonals of the square are \(TV\) and \(UW\).

Step2: Find mid - point of \(TV\)

The mid - point of \(T(0,0)\) and \(V(0,10)\) is \(M_{TV}=(\frac{0 + 0}{2},\frac{0+10}{2})=(0,5)\).

Step3: Find mid - point of \(UW\)

The mid - point of \(U(5,5)\) and \(W(x,y)\) is \(M_{UW}=(\frac{5 + x}{2},\frac{5 + y}{2})\).

Step4: Equate mid - points

Since the mid - points of the diagonals of a square are equal, we have \(\frac{5 + x}{2}=0\) and \(\frac{5 + y}{2}=5\).
From \(\frac{5 + x}{2}=0\), we get \(5+x = 0\), so \(x=-5\).
From \(\frac{5 + y}{2}=5\), we get \(5 + y=10\), so \(y = 5\).

Answer:

\(W(-5,5)\)