A translation of 3 units to the left and 5 units upward shifts every point of a shape or graph accordingly.

To elaborate, a translation is a specific type of transformation that moves each point of a shape or graph a defined distance in a specified direction. When we refer to “3 units left and 5 units up,” we indicate that every point on the shape or graph is relocated 3 units to the left along the x-axis and 5 units upward along the y-axis.

To visualize this, consider a point with coordinates $(x, y)$. After the translation, the new coordinates of this point will be $(x - 3, y + 5)$. This occurs because moving left decreases the x-coordinate, while moving up increases the y-coordinate.

For instance, if you begin with a point at $(4, 2)$, after applying the translation of 3 units to the left and 5 units upward, the new coordinates will be calculated as follows:

$(4 - 3, 2 + 5)$

This simplifies to $(1, 7)$. This translation process is applicable to every point within the shape or graph, ensuring that the entire figure shifts uniformly.

It is important to note that translations do not change the size, shape, or orientation of the figure; they merely reposition it to a new location. This characteristic makes translations a simple yet powerful tool in geometry, aiding in the understanding of how shapes and graphs can be manipulated within the coordinate plane.