Question

Help me to answer this question with vectors, thank you

Answer 1

To find:

The coordinates of a point P such that PA = PB.

Solution:

Given that A(4, 0) and B(0, 9) are the coordinates.

Let the point P is (x,0) because the point is on x-axis, and it is given that |PA| = |PB|.

So,

`√((4-x)^2+(0-0)^2)=√((x-0)^2+(0-9)^2)`

Now, squaring both the sides:

`\begin{gathered} (4-x)^2=x^2+9^2 \\ 16+x^2-8x=x^2+81 \\ 8x=-65 \\ x=(-65)/(8) \end{gathered}`

Thus, the coordinates of point P are (-65/8, 0).