Question

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(grid with x-axis from -6 to 6, y-axis from -6 to 6. point a at (-3, -2), point b at (1, -2), point c at (-3, 5).
point c is located at (-3, 5). at which coordinate point would you place point d to form a rectangle?
○ (-1,5)
○ (1,-3)
○ (1,5)
○ (-1, 3)

Explanation:

Step1: Identify coordinates of A and B

From the graph, Point A is at \((-3, -2)\) and Point B is at \((1, -2)\). Point C is at \((-3, 5)\).

Step2: Recall rectangle properties (opposite sides equal and parallel, same x or y - coordinates for vertical/horizontal sides)

For a rectangle, the sides \(AB\) and \(CD\) should be equal and parallel, and sides \(AC\) and \(BD\) should be equal and parallel.

• The x - coordinate of A and C is \(-3\), so \(AC\) is a vertical line. The x - coordinate of B is \(1\), so the x - coordinate of D should be \(1\) (to make \(BD\) vertical, same as \(AC\)).
• The y - coordinate of C is \(5\), and for \(CD\) to be horizontal (parallel to \(AB\), which has y - coordinate \(-2\) for both A and B, so horizontal line), the y - coordinate of D should be \(5\) (since \(AB\) is horizontal, \(CD\) should also be horizontal, so same y - coordinate as C).

Answer:

(1,5)