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. Reflection across the z-axis: The line containing the points (-2, 3) and (2, 3) is horizontal. When it is reflected across the z-axis, the x-coordinates of the points change sign, while the y-coordinates remain the same. Thus, the reflected points will be (2, 3) and (-2, 3). The length of the line segment can be calculated as:

    \[ \text{Length} = |x_2 - x_1| = |2 - (-2)| = |2 + 2| = 4 \text{ units} \]

    So, the length of the reflected line is 4 units.

  2. Rotation of a line segment 90° clockwise: To rotate a point (x, y) 90° clockwise around the origin, the new coordinates will be (y, -x).

    • For point (2, -1):
      • New coordinates: (-1, -2)
    • For point (5, 4):
      • New coordinates: (4, -5)

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

  3. Translation of a rectangle: A translation does not change the length of the sides. Therefore, if a rectangle has a side that is 10 units long, moving it down 4 units and to the right 5 units will not affect the length of that side. The length of this side will still be 10 units after the translation.