Assume that the shape EFGH is a rectangle, with the following points: E: \( (9,-1) \) \( \mathrm{F}(9,5) \) \( \mathrm{G}:(-6,5) \) \( \mathrm{H}:(x, y) \) What coordinate point should H be so that the shape forms a rectangle? \( (6,-1) \) \( (-6,1) \) \( (6,1) \) \( (-6,-1) \)

To find the coordinates of point H that will complete the rectangle EFGH, we can utilize the properties of rectangles. A rectangle has opposite sides that are parallel and equal in length. Given points E (9, -1), F (9, 5), and G (-6, 5), we know: - EF is vertical (same x-value), and FG is horizontal (same y-value), thus forming part of the rectangle. To find the coordinates of H, we need to determine the point that will keep E, F, G, and H as corners of a rectangle. The x-coordinate for point H should match the x-coordinate of point G (-6), and the y-coordinate should match the y-coordinate of point E (-1). Thus, point H must be (-6, -1), which corresponds to the last available option. Point H should be at the coordinates \( (-6, -1) \). To visualize it: if you plotted points E, F, and G, you'd see how H fits snugly into the rectangle shape, giving you a classic right-angled structure! Isn’t geometry just a fun puzzle?