What is the locus of points equidistant from A and C?

[Ypara]

My answer that I formulated was:

The locus is Point D and B are equidistant to A and C because all sides of a square are congruent & the midpoint of the diagonal of A and C equidistant to both A and C.

 

[Deleted member 4993]

View attachment 13103
My answer that I formulated was:

The locus is Point D and B are equidistant to A and C because all sides of a square are congruent & the midpoint of the diagonal of A and C equidistant to both A and C.

The locus of a point would be:

A line - straight or curved.

So you need to find the equation of the line (straight or curved) where every point on the curve is equidistant from A and C.

For example, the locus of points on a plane, at a constant distance (d) from another given point (h,k) is a circle. The equation of that locus would be:

(x - h)² + (y - k)² = d²

Similarly,

the locus of points in 3-D space, at a constant distance (d) from another given point (h,k,p) is a sphere.

Now think about your problem.....

 

[Dr.Peterson]

View attachment 13103
My answer that I formulated was:

The locus is Point D and B are equidistant to A and C because all sides of a square are congruent & the midpoint of the diagonal of A and C equidistant to both A and C.

It's hard to untangle your grammar to see how close you are to the right idea. Points D and B are on the locus, as is the midpoint of the diagonal, but they are not the entire locus. Where will all such points be? (For example, "the line determined by ...")

You don't need to give an equation, but a complete description, in geometrical terms, will be required.