Answer:
See Below.
Step-by-step explanation:
We are given a point P(x, y). It is equidistant from A(3, 6) and B(-3, 4).
So, let's first determine the distance from P to each point. We can use the distance formula:
Segment PA:
We will let P(x, y) be (x₂, y₂) and A(3, 6) be (x₁, y₁). By substitution:
This represents the distance from P to A.
Segment PB:
Again, we will let P(x, y) be (x₂, y₂) and B(-3, 4) be (x₁, y₁). By the distance formula:
We may simplify:
Now, we know that the two distances are equivalent. Hence:
Simplify. Square both sides:
Square:
Subtract all terms from the right:
Distribute the negative:
Rearrange:
Combine like terms;
We can divide both sides by -4:
Finally, adding 5 to both sides produces: