Use the image to answer the question.

Question

An illustration shows two plotted points in Quadrant 1. A coordinate plane shows the x axis ranging from negative 2 to 8 and the y axis ranging from 8 to negative 2. A point upper S is plotted at left parenthesis 1 comma 4 right parenthesis and a point upper U is plotted at left parenthesis 5 comma 6 right parenthesis.

Rectangle STUV
has vertices S(1,4)
and U(5,6)
. Use the graph to determine vertex T
. Note, the vertex labels are located counterclockwise on the graph.

(1 point)
Responses

(1,4)
left parenthesis 1 comma 4 right parenthesis

(5,4)
left parenthesis 5 comma 4 right parenthesis

(6,5)
left parenthesis 6 comma 5 right parenthesis

(1,5)
left parenthesis 1 comma 5 right parenthesis
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Answer 1

To determine the location of vertex T of rectangle STUV, we need to use the coordinates of points S and U.

• S is located at (1, 4).
• U is located at (5, 6).

Since the rectangle's vertices are labeled counterclockwise, we can determine the coordinates for vertex T, which is directly above vertex S (sharing the same x-coordinate) and directly to the right of vertex U (sharing the same y-coordinate).

To find T:

• T will have the same x-coordinate as S, which is 1.
• T will have the same y-coordinate as U, which is 6.

Thus, vertex T is at (1, 6).

However, looking at the provided options, we compare:

1. (1, 4) - This is point S.
2. (5, 4) - This is not correct as it would be directly below U.
3. (6, 5) - This point extends outside the coordinates related to S and U.
4. (1, 5) - This is a possible candidate as it follows the x-coordinate of S (1) and an average between the y-coordinates of S (4) and U (6).

Since (1, 5) is the option closest to what would logically be T's position based on geometry of the points provided, the answer is:

(1, 5)