Finding the Horizontal Translation of a Quadrilateral on a Coordinate Plane

Published on April 2, 2026

Geometry

Determine the horizontal shift of quadrilateral WXYZ onto W'X'Y'Z' by calculating the difference between corresponding x-coordinates. The shape is translated 5 units to the right.

Question

Answer

To determine the horizontal translation used to move quadrilateral

, we need to compare the coordinates of the corresponding vertices of the two quadrilaterals.

Identify the coordinates of the vertices of the original quadrilateral (the grey shape):
Looking at the grid, we can pick a vertex, for example, .
Vertex is at .
Identify the coordinates of the corresponding vertex of the translated quadrilateral (the darker shape):
Vertex is at .
Calculate the change in position:
The -coordinates remain the same (), which confirms this is purely a horizontal translation.
To find the change in the -coordinate, subtract the original -coordinate from the translated -coordinate: