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To prove the triangles are congruent, which of the following rigid motions would map △GHJ to △ZNP ? (1 point) Responses rotation −90° (clockwise) about point J, then translation along the vector, mapping point H to point Z rotation negative 90 degrees (clockwise) about point upper J , then translation along the vector, mapping point upper H to point upper Z translation along the vector, mapping point J to point P, then rotation −90° (clockwise) about point J translation along the vector, mapping point upper J to point upper P , then rotation negative 90 degrees (clockwise) about point upper J translation along the vector, mapping point J to point P, then rotation 90° (counterclockwise) about point J translation along the vector, mapping point upper J to point upper P , then rotation 90 degrees (counterclockwise) about point upper J translation along the vector, mapping point G to point N, then rotation −90° (clockwise) about point G translation along the vector, mapping point upper G to point upper N , then rotation negative 90 degrees (clockwise) about point upper G

3 answers

To determine which rigid motion maps triangle GHJ to triangle ZNP, analyze the relationships between the triangles' points.

  1. Identify Key Points:

    • For triangle GHJ: Points are G, H, J.
    • For triangle ZNP: Points are Z, N, P.

  2. Establish Rigid Motion Steps:

    • Remember that rigid motions include translations, rotations, and reflections. We need to check potential movements that align corresponding points of the triangles.

  3. Evaluate Each Option:

    • Option 1: Rotate -90° clockwise about point J, then translate mapping H to Z.
    • Option 2: Rotate -90° clockwise about point J, then translate mapping H to Z. Identical to Option 1, but noted differently.
    • Option 3: Translate J to P, then rotate -90° clockwise about J.
    • Option 4: Translate J to P, then rotate -90° clockwise about J. Identical to Option 3, but noted differently.
    • Option 5: Translate J to P, then rotate 90° counterclockwise about J.
    • Option 6: Translate J to P, then rotate 90° counterclockwise about J. Identical to Option 5, but noted differently.
    • Option 7: Translate G to N, then rotate -90° clockwise about G.
    • Option 8: Translate G to N, then rotate -90° clockwise about G. Identical to Option 7, but noted differently.

  4. Choosing the Right Option:

    • If we consider the necessary rotations and the points involved, options utilizing translation and rotation from J to P will likely yield the necessary alignment for congruence with ZNP.

Based on the analysis, the suitable choice would likely involve either directly translating J to P and applying a clockwise rotation around J or G.

Best Options:

  • Translate along the vector, mapping point J to point P, then rotate -90° (clockwise) about point J. This option would align the triangles correctly through the specified rigid motions.

Thus, the option is: Translation along the vector, mapping point J to point P, then rotation -90° (clockwise) about point J.

abcd format

Sure! Based on the analysis of the motions needed to map triangle GHJ to triangle ZNP, here is the response in the requested format (abcd):

a. Rotation -90° clockwise about point J, then translation along the vector, mapping point H to point Z.
b. Rotation -90° clockwise about point J, then translation along the vector, mapping point H to point Z.
c. Translation along the vector, mapping point J to point P, then rotation -90° (clockwise) about point J.
d. Translation along the vector, mapping point J to point P, then rotation -90° (clockwise) about point J.
e. Translation along the vector, mapping point J to point P, then rotation 90° (counterclockwise) about point J.
f. Translation along the vector, mapping point J to point P, then rotation 90° (counterclockwise) about point J.
g. Translation along the vector, mapping point G to point N, then rotation -90° (clockwise) about point G.
h. Translation along the vector, mapping point G to point N, then rotation -90° (clockwise) about point G.

Correct Option:

Option c (or d) would be the right choice:
c. Translation along the vector, mapping point J to point P, then rotation -90° (clockwise) about point J.