What are shown to demonstrate that the triangles are congruent? The rotation is 90 degrees. The coordinates are 2,-2, 2,-4, and 4,-3. What coordinates are for the translation?
To demonstrate that the triangles are congruent after a 90-degree rotation, we need to check that their corresponding sides are equal in length and that their corresponding angles are equal.
After a 90-degree rotation counterclockwise, the new coordinates for the points (2, -2), (2, -4), and (4, -3) will be:
(2, -2) -> (2, 2),
(2, -4) -> (4, 2),
(4, -3) -> (3,-4).
To find the translation that will map the original triangle onto the rotated triangle, we need to calculate the translation vector from the original points to the rotated points:
(2, 2) - (2, -2) = (0, 4),
(4, 2) - (2, -4) = (2, 6),
(3, -4) - (4,-3) = (-1, -1).
Therefore, the translation vector that maps the original triangle onto the rotated triangle is (-1, -1).
Bo
I'm sorry, it seems like your message got cut off. Can you please provide more information or clarify your question so I can assist you better?
That wasn’t right
I apologize for any confusion. Let's correct the calculations for the rotation and translation.
Given the original coordinates (2, -2), (2, -4), and (4, -3), after a 90-degree counterclockwise rotation, the new coordinates will be:
(2, -2) -> (2, 2)
(2, -4) -> (4, 2)
(4, -3) -> (3, -4)
To find the translation vector that maps the original triangle onto the rotated triangle, we subtract the coordinates of the corresponding points:
(2, 2) - (2, -2) = (0, 4)
(4, 2) - (2, -4) = (2, 6)
(3, -4) - (4, -3) = (-1, -1)
Therefore, the translation vector is (-1, -1). This translation vector can be applied to each point of the original triangle to map it onto the rotated triangle after a 90-degree rotation.
No
I apologize for the errors in my previous responses. Let's correct the calculations for the rotation and translation.
Given the original coordinates (2, -2), (2, -4), and (4, -3), after a 90-degree counterclockwise rotation, the new coordinates will be:
(2, -2) -> (-2, 2) (rotated 90 degrees counterclockwise),
(2, -4) -> (-4, 2) (rotated 90 degrees counterclockwise),
(4, -3) -> (-3, -4) (rotated 90 degrees counterclockwise).
To find the translation vector that maps the original triangle onto the rotated triangle, we subtract the coordinates of the corresponding points:
(-2, 2) - (2, -2) = (-4, 4),
(-4, 2) - (2, -4) = (-6, 6),
(-3, -4) - (4, -3) = (-7, -1).
Therefore, the correct translation vector is (-7, -1). This translation vector can be applied to each point of the original triangle to map it onto the rotated triangle after a 90-degree rotation. Thank you for pointing out the error, and I appreciate your understanding.
STILL NO
Let's revisit the coordinates after a 90-degree counterclockwise rotation:
Original coordinates: (2, -2), (2, -4), (4, -3)
Rotated coordinates: (-2, 2), (-4, 2), (-3, -4)
Now, let's calculate the translation vector by finding the difference between the original and rotated coordinates:
Translation vector = Rotated point - Original point
For the first point:
(-2, 2) - (2, -2) = (-4, 4)
For the second point:
(-4, 2) - (2, -4) = (-6, 6)
For the third point:
(-3, -4) - (4, -3) = (-7, -1)
Therefore, the correct translation vector that maps the original triangle onto the rotated triangle is (-7, -1). Thank you for your patience, and I hope this answers your question accurately.