Question

which sequence of transformations constructs the coordinate plane using the first quadrant of the coordinate plane? select all that apply. rotate the first quadrant 180° clockwise three times. translate the first quadrant 1 unit up, 1 unit left, and 1 unit down. translate the first quadrant 1 unit up, 1 unit right and 1 unit down. reflect the first quadrant across the x - axis, across the y - axis, and across the x - axis. reflect the first quadrant across the y - axis and then rotate 90° counter - clockwise. rotate the first quadrant 90° clockwise two times and then reflect across the x - axis.

Explanation:

Step1: Analyze coordinate - plane transformations

Transformations in the coordinate - plane include rotation, reflection, and translation. Rotation changes the orientation of a figure around a point, reflection flips a figure across a line, and translation moves a figure without changing its shape or orientation.

Step2: Evaluate each option

• Rotating the first quadrant 90° clockwise two times will move it to the fourth and then to the third quadrant. Reflecting across the x - axis further changes its position. This sequence does not construct the whole coordinate - plane using only the first quadrant.
• Reflecting the first quadrant across the y - axis gives the second quadrant, then rotating 90° counter - clockwise does not construct the whole plane.
• Reflecting across the x - axis gives the fourth quadrant, across the y - axis gives the second quadrant, and across the x - axis again gives the third quadrant. This sequence constructs the whole coordinate - plane.
• Translating the first quadrant 1 unit up, 1 unit right and 1 unit down just moves the first - quadrant figure without constructing other quadrants.
• Translating 1 unit up, 1 unit left and 1 unit down also just moves the first - quadrant figure.
• Rotating 180° clockwise three times does not construct the whole coordinate - plane.

Answer:

Reflect the first quadrant across the x - axis, across the y - axis, and across the x - axis.