Question
Assume that the shape EFCH is a rectangle, with the following points: E: \( (9,-1) \) F: \( (9,5) \) \( \mathrm{C}:(-6,5) \) H: \( (x, y) \) What coordinate point should H be so that the shape forms a rectangle? \( (6,-1) \) \( (-6,1) \) \( (6,1) \) \( (-6,-1) \)
Ask by Hanson Kelly. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Point H should be at (–6, –1) to form a rectangle.
Solution
For a rectangle, opposite sides must be parallel and equal in length.
We are given the following three points:
• E = (9, –1)
• F = (9, 5)
• C = (–6, 5)
Since a rectangle has adjacent sides that are perpendicular and opposite sides that are parallel, we can analyze the sides:
1. Segment EF: From (9, –1) to (9, 5) is a vertical line (x remains constant at 9).
2. Segment FC: From (9, 5) to (–6, 5) is a horizontal line (y remains constant at 5).
Therefore, to complete the rectangle, the fourth vertex H must be positioned such that:
• It is directly horizontally in line with E (which has y = –1).
• It is directly vertically in line with C (which has x = –6).
Hence, H should be at (–6, –1).
Thus, the correct answer is (–6, –1).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To ensure that EFCH forms a rectangle, we need to find point H such that both EF and CH are parallel (and equal in length), while EH and FC are also parallel (and equal in length). Given that E and F share the same x-coordinate (9), they define a vertical line, while C shares the y-coordinate with F (5). To keep H aligned correctly, its x-coordinate must be the same as C, which is -6. The y-coordinate of H should match E's y-coordinate to maintain parallelism with line EF, which is -1. Therefore, point H should be at (-6,-1). Your answer for H is: \( (-6, -1) \).
