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The figures given are congruent. Find a sequence of rigid motions that maps one figure to the other.

5. BCDE: (6, 2), (8, 2), (6, 6), (–2, 6) to FGHI: (2, -4), (4, –4), (2, –8), (–6, –8)

6. JKLM: (1,8), (4, 4), (-2,-2), (-2, 6) to OPQR: (5, -1), (1,-4), (-5, 2), (3, 2)​

1 Answer

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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.

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