A line segment with endpoints A(–4, 3, 2) and B(5, –6, –1) is translated first 2 units back, 3 units right, and 1 unit up. The image is then translated 7 units to the left. What are the coordinates of B´?
A: (3, 4, 0)
B: (3, –10, 0)
C: (5, –6, –1)
D: (–4, –10, –7)
Please help, I do not know how to figure this out! Thank you!
all you have to look at is B(5,-6,-1)
If you are using the standard position of x-axis towards and away from you, the y-axis left and right, and the z-axis up and down, then
B ---> 2 units back, 3 units right, and 1 unit up ---> B' (3, -3, 0) ,
then B'(3,-3,0) --> 7 units to the left ---> B'(3,-10,0)
To find the coordinates of B´, we need to perform two translations: one initial translation and one final translation.
Step 1: Initial Translation
The initial translation is 2 units back, 3 units right, and 1 unit up. To perform this translation on point B(5, -6, -1), we need to subtract the corresponding values.
New x-coordinate = 5 - 2 = 3
New y-coordinate = -6 + 3 = -3
New z-coordinate = -1 + 1 = 0
So, after the initial translation, the coordinates of B´ are (3, -3, 0).
Step 2: Final Translation
The final translation is 7 units to the left. To perform this translation on B´(3, -3, 0), we need to subtract 7 from the x-coordinate.
New x-coordinate = 3 - 7 = -4
New y-coordinate remains the same: -3
New z-coordinate remains the same: 0
So, after the final translation, the coordinates of B´ become (-4, -3, 0).
Therefore, the correct answer is option D: (–4, -3, 0).
To find the coordinates of B´, we need to follow the given translation steps.
1. Translate first 2 units back: To do this, we subtract 2 from the z-coordinate of point B. The new coordinates of B become (5, -6, -1 - 2) = (5, -6, -3).
2. Translate 3 units right: We add 3 to the x-coordinate of point B. The new coordinates of B´ become (5 + 3, -6, -3) = (8, -6, -3).
3. Translate 1 unit up: We add 1 to the y-coordinate of point B´. The new coordinates of B´ become (8, -6 + 1, -3) = (8, -5, -3).
4. Translate 7 units to the left: We subtract 7 from the x-coordinate of point B´. The final coordinates of B´ become (8 - 7, -5, -3) = (1, -5, -3).
Therefore, the coordinates of B´ are (1, -5, -3).
Comparing the answer choices:
A: (3, 4, 0) - Incorrect
B: (3, -10, 0) - Incorrect
C: (5, -6, -1) - Incorrect
D: (-4, -10, -7) - Incorrect
None of the given options matches the coordinates of B´, so none of the answer choices is correct.