Congruent Figures Practice

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A coordinate plane with 4 quadrants shows x and y axes ranging from negative 9 to 9 in increments of 1. Three rectangles are formed by lines joining four plotted points each. The coordinates of the plotted points for first rectangle joined by solid lines are left parenthesis negative 5 comma negative 4 right parenthesis, left parenthesis negative 1 comma negative 4 right parenthesis, left parenthesis negative 1 comma negative 6 right parenthesis, and left parenthesis negative 5 comma negative 6 right parenthesis. The coordinates for the second rectangle joined by lines made of dashes and dots are left parenthesis 3 comma 4 right parenthesis, left parenthesis 5 comma 4 right parenthesis, left parenthesis 5 comma 8 right parenthesis, and left parenthesis 3 comma 8 right parenthesis. The coordinates of the plotted points for the third rectangle joined by dotted lines are left parenthesis negative 4 comma 1 right parenthesis, left parenthesis negative 6 comma 1 right parenthesis, left parenthesis negative 6 comma 5 right parenthesis, and left parenthesis negative 4 comma 5 right parenthesis.
The first step to determine that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I was to rotate the first rectangle 90 degrees clockwise about the origin. What is the next step?

(1 point)

Answer 1

To determine the next step after rotating the rectangle in Quadrant III (the first rectangle) 90 degrees clockwise about the origin, you need to translate the coordinates of the rotated rectangle to match the position of the rectangle in Quadrant I (the second rectangle).

Here are the steps you would follow:

1. Rotate the Rectangle: You already performed this by rotating the coordinates of the rectangle in Quadrant III (which are \((-5, -4)\), \((-1, -4)\), \((-1, -6)\), and \((-5, -6)\)) 90 degrees clockwise. After rotation, the new coordinates would be \((4, -5)\), \((4, -1)\), \((6, -1)\), and \((6, -5)\).

2. Translate the Rotated Rectangle: Next, you need to shift the rectangle to the correct position in Quadrant I. You can do this by translating the coordinates up and to the right until they match the position of the rectangle in Quadrant I.

For instance, you would translate the rectangle up by adding a specific value to the y-coordinates and move the rectangle right by adding to the x-coordinates until you align the vertices of the rotated rectangle with the corresponding vertices of the rectangle in Quadrant I.

Thus, the next step is to translate the rotated rectangle to match the position of the rectangle in Quadrant I.