Triangle ABC is reflected across the y axis to produce triangle DEF. Which segment on DEF is congruent to the segment BC? B is on 6 y axis and 3 on x axis and C is 2 y axis and 6 x axis
segment EF
To find the segment on DEF that is congruent to segment BC after reflecting triangle ABC across the y-axis, we need to find the corresponding points on DEF.
Given that point B is located at (3, 6) and point C is located at (6, 2), when reflected across the y-axis, the x-coordinates of these points will change their signs but the y-coordinates will remain the same.
Reflecting point B, we get (-3, 6), and reflecting point C, we get (-6, 2).
The segment on DEF that is congruent to segment BC is the segment joining the reflected points. So, the segment DE is congruent to segment BC.
When triangle ABC is reflected across the y-axis, all the points will have the same x-coordinate but opposite y-coordinates. In other words, the x-coordinates will remain the same, and the y-coordinates will have the opposite sign.
The x-coordinate of point B is 3, so after reflecting across the y-axis, the x-coordinate of the corresponding point D will also be 3.
The y-coordinate of point B is 6, so after reflection, the y-coordinate of the corresponding point D will be -6.
Thus, the corresponding point to B in triangle DEF is D(3, -6).
The corresponding segment to BC is therefore segment DE, with coordinates D(3, -6) and E(2, -2).