Question

Points A, P and B are collinear on AB, and PB:AB= 2/7. A is located at the orgin, P is located at (10,-5) and B is located at (x,y). Which axis is closer to B , the axis or the y-axis ?

Answer 1

well, we don't really need to find what point B is

find the equation of the line containing (0,0) and (10,-5)
if the slope is 1, then point B is equidistant from the x and y axis
if the slope is greater than 1, then point B is closer to the y axis
if the slope is less than 1, then point B is closer to the x axis


slope between (0,0) and (10,-5) is (-5-0)/(10-0)=-5/10=-1/2
the slope is less than 1
it is closer to the x axis

Answer 2

A (0,0) is at the origin.
P is at (10, -5).

Let the coordinates of B be (x,y).
Because A, B, and P are collinear and PB : AB = 2/7, therefore
x = (7/9)*10 = 7.78
y = (7/9)*(-5) = -3.89

The distance between B and the x-axis is 3.89
The distance between B and the y-axis s 7.78

Answer: The x-axis is closer to B