Question
A coordinate plane's x-axis ranges from negative 7 to 10 and its y-axis ranges from negative 3 to 7, both by 1-unit increments. 6 points are marked and plotted forming 2 triangles, 1 dotted and 1 solid.
Determine whether triangle DEF
is a translation of triangle ABC
. Enter the number of the correct statement.
Statement #1: Triangle DEF
is a translation of triangle ABC
because each point is translated 8 units to the right and 2 units down.
Statement #2: Triangle DEF
is not a translation of triangle ABC
because the triangles are not congruent.
(1 point)
Statement #
is correct.
Determine whether triangle DEF
is a translation of triangle ABC
. Enter the number of the correct statement.
Statement #1: Triangle DEF
is a translation of triangle ABC
because each point is translated 8 units to the right and 2 units down.
Statement #2: Triangle DEF
is not a translation of triangle ABC
because the triangles are not congruent.
(1 point)
Statement #
is correct.
Answers
GPT-4o mini
To determine the correctness of the statements regarding triangles ABC and DEF, we need to consider the definition of translation in geometry. A translation is a transformation that shifts every point of a shape or object a fixed distance in a specified direction. This means that for triangle DEF to be a translation of triangle ABC, each vertex of triangle ABC must be moved the same distance in the same direction to obtain the corresponding vertex in triangle DEF.
**Statement #1** claims that triangle DEF is a translation of triangle ABC because each point is translated 8 units to the right and 2 units down. If this is true, then all corresponding points of the triangles should indeed have that same transformation applied.
**Statement #2** claims that triangle DEF is not a translation of triangle ABC because the triangles are not congruent. This statement focuses on the congruence issue rather than the translational movement. If statement #1 is correct and the translation has been accurately applied, then by definition, triangle DEF would be congruent to triangle ABC, as translations do not alter the sizes or angles of shapes.
If it turns out that all points have indeed been moved by that same vector (8 right and 2 down), then statement #1 would be correct, and statement #2 would be incorrect. If, however, the triangles differ in shape or size after considering the claimed translation, then statement #2 would be correct, indicating triangle DEF is not congruent to triangle ABC, but that would imply that the translation claiming in statement #1 is incorrect.
Ultimately, it will depend on verifying whether the translation described in statement #1 holds true. However, without the actual coordinates of points A, B, C, D, E, and F, we cannot definitively assess the correctness of either statement.
If you were asking to choose between the statements based solely on the information provided, the correct statement would likely be Statement #1, as it specifies a transformational movement that, if true, aligns with the definition of a translation.
**Final Answer:** Statement #1 is correct. (If the points indeed reflect the translation described.)
**Statement #1** claims that triangle DEF is a translation of triangle ABC because each point is translated 8 units to the right and 2 units down. If this is true, then all corresponding points of the triangles should indeed have that same transformation applied.
**Statement #2** claims that triangle DEF is not a translation of triangle ABC because the triangles are not congruent. This statement focuses on the congruence issue rather than the translational movement. If statement #1 is correct and the translation has been accurately applied, then by definition, triangle DEF would be congruent to triangle ABC, as translations do not alter the sizes or angles of shapes.
If it turns out that all points have indeed been moved by that same vector (8 right and 2 down), then statement #1 would be correct, and statement #2 would be incorrect. If, however, the triangles differ in shape or size after considering the claimed translation, then statement #2 would be correct, indicating triangle DEF is not congruent to triangle ABC, but that would imply that the translation claiming in statement #1 is incorrect.
Ultimately, it will depend on verifying whether the translation described in statement #1 holds true. However, without the actual coordinates of points A, B, C, D, E, and F, we cannot definitively assess the correctness of either statement.
If you were asking to choose between the statements based solely on the information provided, the correct statement would likely be Statement #1, as it specifies a transformational movement that, if true, aligns with the definition of a translation.
**Final Answer:** Statement #1 is correct. (If the points indeed reflect the translation described.)