translate quadrilateral ABCD by 2 u it’s to the right and 2 and 4 units up. which of the following are the coordinates of new quadrilateral A’B’C’D’. A.) A’(7,-1),B’(10,1)C’(12,-1),D’(10,-3), B.) A’(7,7),B’(10,9),C’(12,7),D’(10,5), C.) A’(3,-1),B’(6,1),C’(8,-1),D’(6,-3), D.) A’(3,7),B’(6,9),C’(8,7),D’(6,5)
To translate quadrilateral ABCD by 2 units to the right and 2 units up, we need to add 2 to the x-coordinate and 2 to the y-coordinate of each of the original coordinates.
The original coordinates are:
A(5, -3)
B(8, -1)
C(10, -3)
D(8, -5)
Adding 2 to the x-coordinate and 2 to the y-coordinate of each original coordinate, we get the new coordinates:
A' = (5 + 2, -3 + 2) = (7, -1)
B' = (8 + 2, -1 + 2) = (10, 1)
C' = (10 + 2, -3 + 2) = (12, -1)
D' = (8 + 2, -5 + 2) = (10, -3)
So the correct answer is:
A.) A’(7,-1), B’(10,1), C’(12,-1), D’(10,-3)
Using the given information, the translation applied to the coordinates is +2 in the x-direction (to the right) and +2 in the y-direction (up).
To find the new coordinates for A', we add 2 to the x-coordinate and add 2 to the y-coordinate of A: A'(1+2, 2+2) = A'(3, 4).
To find the new coordinates for B', we add 2 to the x-coordinate and add 2 to the y-coordinate of B: B'(4+2, 0+2) = B'(6, 2).
To find the new coordinates for C', we add 2 to the x-coordinate and add 2 to the y-coordinate of C: C'(2+2, -2+2) = C'(4, 0).
To find the new coordinates for D', we add 2 to the x-coordinate and add 2 to the y-coordinate of D: D'(1+2, -4+2) = D'(3, -2).
Thus, the new coordinates for quadrilateral A'B'C'D' are: A'(3, 4), B'(6, 2), C'(4, 0), D'(3, -2).
Therefore, option C.) A’(3,-1), B’(6,1), C’(8,-1), D’(6,-3) is the correct answer.
To translate a figure, you need to shift each coordinate of the original figure by a certain distance. In this case, we are shifting by 2 units to the right and 2 units up.
To find the new coordinates of each vertex, add 2 to the x-coordinate (rightward shift) and add 2 to the y-coordinate (upward shift).
Let's apply this to each vertex of the original quadrilateral ABCD:
A(1, 1):
A'(1 + 2, 1 + 2) = A'(3, 3)
B(4, 1):
B'(4 + 2, 1 + 2) = B'(6, 3)
C(6, -1):
C'(6 + 2, -1 + 2) = C'(8, 1)
D(3, -1):
D'(3 + 2, -1 + 2) = D'(5, 1)
Now let's compare the new coordinates of the vertices of the translated quadrilateral with the given options:
A.) A’(7,-1), B’(10,1), C’(12,-1), D’(10,-3)
B.) A’(7,7), B’(10,9), C’(12,7), D’(10,5)
C.) A’(3,-1), B’(6,1), C’(8,-1), D’(6,-3)
D.) A’(3,7), B’(6,9), C’(8,7), D’(6,5)
Comparing the new coordinates with the options, we see that the correct answer is Option C:
A’(3,-1), B’(6,1), C’(8,-1), D’(6,-3)