A line containing the points (-2, 3) and (2, 3) is reflected across the z-axis. How long is the reflected line? (1 point)

3 units

infinitely long

4 units

not enough information

A line segment has endpoints (2,-1) and (5,-4). What are the new endpoints after rotating the segment 90" clockwise? (1 point)

(-1,-2) and (-4, -5)

(-2,-1) and (-5, -4)

(2,1) and (4, 5)

(-2, 1) and (-5, 4)

A rectangle has a side that is 10 units long. How long will this side be after the figure is translated down 4 units and to the right 5 units?

1 answer

  1. Length of the reflected line: A line containing the points (-2, 3) and (2, 3) is horizontal with a constant y-value of 3. The line has endpoints that distance of 4 units because: \[ \text{Distance} = |x_2 - x_1| = |2 - (-2)| = |2 + 2| = 4 \] When reflected across the z-axis, the y-value remains constant, and the x-values change sign. So the reflected endpoints are (2, 3) and (-2, 3), maintaining a length of 4 units.

    Answer: 4 units

  2. New endpoints after rotating the segment 90° clockwise: To rotate a point (x, y) 90° clockwise about the origin, the new coordinates become (y, -x).

    For the endpoints (2, -1):

    • New coordinates = (-1, -2)

    For the endpoints (5, -4):

    • New coordinates = (-4, -5)

    Therefore, the new endpoints after a 90° clockwise rotation are (-1, -2) and (-4, -5).

    Answer: (-1, -2) and (-4, -5)

  3. Length of a rectangle side after translation: Translation does not affect the length of sides of a figure. The length remains constant regardless of its position. Thus, a side that is 10 units long will still be 10 units long after being translated down 4 units and to the right 5 units.

    Answer: 10 units