Final answer:
The translated vertices of Triangle XYZ after moving 5 units left and 3 units up are X(-4, 1), Y(-2, -2), and Z(-1, 4). The new positions are calculated by subtracting 5 from the x-coordinates and adding 3 to the y-coordinates of the original vertices.
Step-by-step explanation:
The question asks about the result of translating Triangle XYZ with given vertices (X, Y, and Z) 5 units left and 3 units up on the Cartesian plane. A translation in geometry means to move every point of a shape in the same direction and by the same amount. The vertices of the translated triangle can be found by subtracting 5 from the x-coordinates and adding 3 to the y-coordinates of Triangle XYZ's vertices.
To perform the translation of point X(1,-2):
Translated X = (1 - 5, -2 + 3) = (-4, 1)
To perform the translation of point Y(3,-5):
Translated Y = (3 - 5, -5 + 3) = (-2, -2)
To perform the translation of point Z(4,1):
Translated Z = (4 - 5, 1 + 3) = (-1, 4)
Therefore, the new coordinates of the translated triangle XYZ are X(-4, 1), Y(-2, -2), and Z(-1, 4).