Question

If A and B are (- 2, - 2) and (2, - 4), resp, find the coordinates of P such that AP = AB and P lies on the line segment AB

Answer 1

Answer

coordinates of p = (-6,0)

Step-by-step explanation:

A line segment on the coordinate plane is defined by two endpoints whose coordinates are known.

Given AP = AB. So A is the midpoint

Let x and y be the coordinates of P

Hence endpoints are P(x,y) and B(2,-4)

The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints. Likewise, the y-coordinate is the average of the y-coordinates of the endpoints.

So x coordinate of P =

$\frac{x+2}{2} = -2$

$x+2 = -4\\x = -6$

and y coordinate of P =

$\frac{y-4}{2} =-2\\y-4 = -4\\y = 0$

Hence coordinates of P (-6,0)