Question

Given the vertices A(−3,4)
, B(8,4)
, and C(8,−7)
, which of the following is the final point needed to construct a square? (1 point)
Responses

(8,−7)
left parenthesis 8 comma negative 7 right parenthesis

(8,4)
left parenthesis 8 comma 4 right parenthesis

(−3,−7)
left parenthesis negative 3 comma negative 7 right parenthesis

(−3,4)

Answers

Answered by GPT-4o mini
To find the final point needed to construct a square from the vertices A(-3, 4), B(8, 4), and C(8, -7), we can first identify the points we have:

1. A(-3, 4)
2. B(8, 4)
3. C(8, -7)

We can see that points A and B form a horizontal line segment at y = 4, while point C is below the line segment (at y = -7) and vertically aligned with point B.

For a square, we need one more point that forms a right angle with the existing points. Based on the given vertices, the fourth point would need to maintain equal distance from the other vertices.

The missing point D can be calculated as either:

1. Move vertically down from A to complete the square. This would give us D(-3, -7).
2. Move to the right from C horizontally to meet the same y-axis level as A. This would give us D(8,4), but since B is already there, it doesn't add a new point.

The point that completes the square formed by the existing points and maintains square properties is D(-3, -7).

Thus, the correct answer for the final point needed to construct the square is:

**(−3,−7)**.

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