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An illustration shows a coordinate plane. The x-axis and the y-axis range from negative 6 to 6 in one unit increments. Six points are plotted on the plane. Two right triangles are graphed on the plane. Three points are plotted in the first quadrant. Point A is plotted at the coordinates left parenthesis 3 comma 2 right parenthesis, Point B is plotted at left parenthesis 3 comma 6 right parenthesis, and point C is plotted at left parenthesis 6 comma 2 right parenthesis. Points A and B, points B and C, and points C and A are connected by a dotted line segment to form triangle A B C. Three points are plotted in the second quadrant. Point D is plotted at the coordinates left parenthesis negative 3 comma 2 right parenthesis, Point E is plotted at left parenthesis negative 3 comma 6 right parenthesis, and point F is plotted at left parenthesis negative 6 comma 2 right parenthesis. Points D and E, points E and F, and points F and D are connected by line segments to form triangle D E F.Triangle ABCis reflected across the y-axis to produce triangle DEF. Which segment on DEF is congruent to the segment BC?(1 point)

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To determine which segment on triangle DEF is congruent to segment BC of triangle ABC, we first need to find the coordinates of the points forming triangle ABC and triangle DEF.

Triangle ABC:

  • Point A: (3, 2)
  • Point B: (3, 6)
  • Point C: (6, 2)

Now, we can find the length of segment BC:

  • Segment BC connects points B and C.
  • Length of BC = |y2 - y1| = |6 - 2| = 4.

Reflection across the y-axis: The reflection of a point (x, y) across the y-axis is (-x, y).

  • Reflecting Point A (3, 2): A' = (-3, 2)
  • Reflecting Point B (3, 6): B' = (-3, 6)
  • Reflecting Point C (6, 2): C' = (-6, 2)

So, triangle DEF is formed by:

  • Point D: (-3, 2) (which is A')
  • Point E: (-3, 6) (which is B')
  • Point F: (-6, 2) (which is C')

Triangle DEF:

  • Points are: D (-3, 2), E (-3, 6), and F (-6, 2).

Next, we find the lengths of the segments in triangle DEF to identify the congruent segment to BC.

  • Segment DE connects points D and E:

    • Length of DE = |y2 - y1| = |6 - 2| = 4.

  • Segment EF connects points E and F:

    • Length of EF = |(-6) - (-3)| = |-3| = 3.

  • Segment FD connects points F and D:

    • Length of FD = |(-3) - (-6)| = |3| = 3.

From our calculations, we see that segment DE in triangle DEF has a length of 4, which is equal to the length of segment BC in triangle ABC.

Conclusion: The segment on triangle DEF that is congruent to segment BC is segment DE.