Question
8. Is there a parallel translation in which the point M (3; - 5) goes to the point N (1; -4), and the point K (0; 0) - to the point L(-2; 1)?
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Answer to a math question 8. Is there a parallel translation in which the point M (3; - 5) goes to the point N (1; -4), and the point K (0; 0) - to the point L(-2; 1)?
Adonis
4.4105 Answers
Solution:
1. To find if a translation exists, the translation vector should be the same for both points.
2. Calculate the translation vector for pointsM N
- Translation vector:\vec{T_1} = (N_x - M_x, N_y - M_y) = (1 - 3, -4 + 5) = (-2, 1)
3. Calculate the translation vector for pointsK L
- Translation vector:\vec{T_2} = (L_x - K_x, L_y - K_y) = (-2 - 0, 1 - 0) = (-2, 1)
4. Compare the translation vectors:
-\vec{T_1} = (-2, 1)
-\vec{T_2} = (-2, 1)
5. Since\vec{T_1} = \vec{T_2}
6. Hence, the parallel translation exists and it is given by the vector(-2, 1)
1. To find if a translation exists, the translation vector should be the same for both points.
2. Calculate the translation vector for points
- Translation vector:
3. Calculate the translation vector for points
- Translation vector:
4. Compare the translation vectors:
-
-
5. Since
6. Hence, the parallel translation exists and it is given by the vector
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