Question

A square has an area of 16 units. One vertex of the square is located at (-5,6). Which of the following could be the coordinates of another possible vertex?(1 point)
Responses

(-5,-6)
(-5,-6)

(3,-3)
(3,-3)

(6,5)
(6,5)

(1,6)

Answer 1

To find the coordinates of another possible vertex of the square, we first need to determine the side length of the square. Given that the area of the square is 16 square units, we can find the side length \(s\) by using the formula for the area of a square:

\[
s^2 = 16 \implies s = 4
\]

Next, we consider the point (-5, 6), which is one vertex of the square. From this vertex, we can find the potential positions of the other vertices. The movement to reach any other vertex from (-5, 6) will be either horizontally or vertically (orthogonal movements) by a distance of 4 units since the side length is 4.

The possible coordinates of the other vertices moving 4 units away from (-5, 6) would be:

1. Move 4 units left:
\[
(-5 - 4, 6) = (-9, 6)
\]

2. Move 4 units right:
\[
(-5 + 4, 6) = (-1, 6)
\]

3. Move 4 units down:
\[
(-5, 6 - 4) = (-5, 2)
\]

4. Move 4 units up:
\[
(-5, 6 + 4) = (-5, 10)
\]

Additionally, we can have diagonal movements. However, as these also pertain to a square's vertex, their calculation involves moving both horizontally and vertically, which is not necessary to check for the given options.

Now to check the provided options:

1. (-5, -6): This point is 12 units down from (-5, 6), which is too far.
2. (3, -3): This does not follow the movements specified (too far).
3. (6, 5): This does not follow the movements specified (too far).
4. (1, 6): This point is 6 units right from (-5, 6), which again is too far.

None of the provided answers are valid vertices of the square based on the calculations.

Therefore, a coordinate like (-9, 6), (-1, 6), (-5, 2), or (-5, 10) would be a possible vertex, but none of the choices you provided fit this criterion.