Final answer:
To make ABDC a rhombus, point A should be located at (4,1), forming equal side lengths with the other points.
Step-by-step explanation:
To find the coordinate point for A that would make ABDC a rhombus, we must remember that a rhombus is a four-sided shape where all sides have equal lengths. Given points B (1,3), C (3,0), and D (4,0), we know that CDs side length is 1 unit because D and C have the same y-coordinate but their x-coordinates are 1 unit apart.
Since AD must be equal to BC and CD due to the properties of a rhombus, A must also be 1 unit away from D in the y-direction, maintaining the same x-coordinate as D. Consequently, A must be at (4,1).
Therefore, point A that would make ABDC a rhombus is at the coordinates (4,1). To confirm this, we can check the distance between A and B, and B and C, since the lengths AB and BC should be equal in a rhombus. The same logic applies to sides AD and CD.