A translation of (4, -5) maps JKLM to OPQR.
To find a sequence of rigid motions that maps one figure onto another (assuming they're congruent), you'll typically use translations, rotations, and reflections.
Let's tackle these problems step by step:
Problem 5: BCDE to FGHI
Given the coordinates:
BCDE: (6, 2), (8, 2), (6, 6), (–2, 6)
FGHI: (2, -4), (4, –4), (2, –8), (–6, –8)
Translation: The shapes seem to have shifted. To match the corresponding points, you might need to shift the points in the BCDE shape.
The x-coordinate has decreased by 4 units, and the y-coordinate has decreased by 6 units from BCDE to FGHI. Hence, a translation of (-4, -6) could map BCDE to FGHI.
Apply the translation to the points of BCDE:
(6, 2) translated by (-4, -6) becomes (6 - 4, 2 - 6) = (2, -4)
(8, 2) translated by (-4, -6) becomes (8 - 4, 2 - 6) = (4, -4)
(6, 6) translated by (-4, -6) becomes (6 - 4, 6 - 6) = (2, -8)
(–2, 6) translated by (-4, -6) becomes (-2 - 4, 6 - 6) = (-6, -8)
So, a translation of (-4, -6) maps BCDE to FGHI.
Problem 6: JKLM to OPQR
Given the coordinates:
JKLM: (1, 8), (4, 4), (-2, -2), (-2, 6)
OPQR: (5, -1), (1, -4), (-5, 2), (3, 2)
Translation: Similar to the previous problem, you can observe the translation needed.
The x-coordinate has increased by 4 units, and the y-coordinate has decreased by 5 units from JKLM to OPQR. So, a translation of (4, -5) could map JKLM to OPQR.
Apply the translation to the points of JKLM:
(1, 8) translated by (4, -5) becomes (1 + 4, 8 - 5) = (5, 3)
(4, 4) translated by (4, -5) becomes (4 + 4, 4 - 5) = (8, -1)
(-2, -2) translated by (4, -5) becomes (-2 + 4, -2 - 5) = (2, -7)
(-2, 6) translated by (4, -5) becomes (-2 + 4, 6 - 5) = (2, 1)
So, a translation of (4, -5) maps JKLM to OPQR.