Question

Triangle XYZ has vertices X = (-1, 7), Y = (1, 1), and Z = (3, 8). Triangle X'Y'Z' is formed when triangle XYZ is shifted right 4 units and up 2 units. What are the coordinates of triangle X'Y'Z' ? Select one: X’ = (-5, 9), Y’ = (-3, 3), and Z’ = (-1, 10) X’ = (-5, 5), Y’ = (-3, -1), and Z’ = (-1, 6) X’ = (3, 9), Y’ = (5, 3), and Z’ = (7, 10) X’ = (1, 11), Y’ = (3, 5), and Z’ = (5, 12)

Answer 1

The shifted coordinates of triangle X'Y'Z' are X' = (3, 9), Y' = (5, 3), and Z' = (7, 10) after adding 4 to each x-coordinate and 2 to each y-coordinate of the original triangle XYZ.

Step-by-step explanation:

To find the coordinates of triangle X'Y'Z' when triangle XYZ is shifted, we need to apply a translation to each vertex of the triangle. This is done by adding the respective units we're shifting to the original coordinates. The original coordinates for X, Y, and Z are (-1, 7), (1, 1), and (3, 8) respectively. Shifting the triangle right by 4 units and up by 2 units means we add 4 to the x-coordinate and 2 to the y-coordinate of each vertex.

• For vertex X: (-1 + 4, 7 + 2) = (3, 9)
• For vertex Y: (1 + 4, 1 + 2) = (5, 3)
• For vertex Z: (3 + 4, 8 + 2) = (7, 10)

The coordinates of triangle X'Y'Z' after the translation are X' = (3, 9), Y' = (5, 3), and Z' = (7, 10).