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. (10, 0)
b. (5, -5)
c. (-5, -5)
d. (-5, 5)

Explanation:

Step1: Recall properties of a square

In a square, the sides are equal in length and perpendicular to each other. The mid - point of the diagonal TV is the same as the mid - point of the diagonal UW.

Step2: Find the mid - point of TV

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For points $T(0,0)$ and $V(0,10)$, the mid - point $M$ of TV is $(\frac{0 + 0}{2},\frac{0+10}{2})=(0,5)$.

Step3: Let the coordinates of $W$ be $(x,y)$

Since the mid - point of UW is the same as the mid - point of TV. For points $U(5,5)$ and $W(x,y)$, using the mid - point formula $(\frac{5 + x}{2},\frac{5 + y}{2})=(0,5)$.

Step4: Solve for $x$ and $y$

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:

D. (-5, 5)