If the distance of P x, y from the points A (3, 6) and B −3, 4 are equal, prove that
3x + y = 5

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:

95.03 is the answer. hope this !