Question

A is at (-2, 1) and B is at (4, -1).

P is a point on y-axis which is equidistant from A and B.
What are the coordinates of P?

Answer 1

The coordinates of P are (1,0)

Explanation:

Midpoint

The midpoint (xm,ym) of a segment defined by points (x1,y1) and (x2,y2) is calculated as follows:

`\displaystyle x_m=(x_1+x_2)/(2)`

`\displaystyle y_m=(y_1+y_2)/(2)`

We need to find the coordinates of P which is equidistant from the endpoints A=(-2,1) and B=(4,-1).

Calculate the midpoint:

`\displaystyle x_m=(-2+4)/(2)=1`

`\displaystyle y_m=(1-1)/(2)=0`

Thus, the coordinates of P are (1,0)

Note the midpoint does not lie on the y-axis but on the x-axis.