∆ XYZ has vertices X(5, 6), Y(9, 12), and Z(12, 8). It is translated right 8 units and up 3 units. What are the coordinates of X’, Y’, and Z’?
A. X' (13, 9), Y' (15, 17), Z' (11, 20)
B. X' (–3, 3), Y' (1, 9), Z' (4, 5)
C. X' (8, 14), Y' (12, 20), Z' (23, 19)
D. X' (13, 9), Y' (17, 15), Z' (20, 11)
D. X' (13, 9), Y' (17, 15), Z' (20, 11)
To find the coordinates of the translated vertices, we need to add the translation values to the original coordinates.
Given that the translation is 8 units to the right and 3 units up, we can add 8 to the x-coordinate and 3 to the y-coordinate of each vertex.
For vertex X(5, 6),
the x-coordinate of X' = 5 + 8 = 13,
the y-coordinate of X' = 6 + 3 = 9.
So, X' is located at (13, 9).
For vertex Y(9, 12),
the x-coordinate of Y' = 9 + 8 = 17,
the y-coordinate of Y' = 12 + 3 = 15.
So, Y' is located at (17, 15).
For vertex Z(12, 8),
the x-coordinate of Z' = 12 + 8 = 20,
the y-coordinate of Z' = 8 + 3 = 11.
So, Z' is located at (20, 11).
Therefore, the correct choice is:
D. X' (13, 9), Y' (17, 15), Z' (20, 11).
To translate a point right and up, you add the translation values to the original coordinates. Here's how to find the coordinates of X', Y', and Z':
X':
X coordinate of X' = X coordinate of X + right translation value = 5 + 8 = 13
Y coordinate of X' = Y coordinate of X + up translation value = 6 + 3 = 9
So, X' is (13, 9).
Y':
X coordinate of Y' = X coordinate of Y + right translation value = 9 + 8 = 17
Y coordinate of Y' = Y coordinate of Y + up translation value = 12 + 3 = 15
So, Y' is (17, 15).
Z':
X coordinate of Z' = X coordinate of Z + right translation value = 12 + 8 = 20
Y coordinate of Z' = Y coordinate of Z + up translation value = 8 + 3 = 11
So, Z' is (20, 11).
Therefore, the correct answer is D. X' (13, 9), Y' (17, 15), Z' (20, 11).