The locus of a point on rhombus ABCD, so that it is equidistant from B and D

Answer

To find the locus of a point on rhombus ABCD that is equidistant from points B and D, we can follow these steps:

### Step-by-Step Solution:

1. **Draw the Rhombus**: Start by sketching rhombus ABCD. Label the vertices A, B, C, and D in clockwise order.

2. **Draw the Diagonals**: Draw the diagonals AC and BD. The diagonals of a rhombus bisect each other at right angles.

3. **Identify Points B and D**: Mark points B and D on your diagram. These are the points from which we want to find the locus of points that are equidistant.

4. **Locate the Midpoint O**: The intersection point of the diagonals (let's call it O) is the midpoint of both diagonals. Since the diagonals bisect each other, O is equidistant from points B and D.

5. **Understand the Concept of Equidistance**: A point that is equidistant from two points lies on the perpendicular bisector of the line segment joining those two points. Therefore, we need to find the perpendicular bisector of segment BD.

6. **Draw the Perpendicular Bisector**: Construct the perpendicular bisector of line segment BD. This line will pass through point O and will be perpendicular to line BD.

7. **Identify the Locus**: Since O is the midpoint and the perpendicular bisector of BD represents all points that are equidistant from B and D, the locus of points that are equidistant from B and D will be the line represented by the perpendicular bisector.

8. **Conclusion**: The locus of the point on rhombus ABCD that is equidistant from points B and D is the line segment AC (the diagonal of the rhombus).

### Final Answer:
The locus of a point on rhombus ABCD that is equidistant from points B and D is the diagonal AC.

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