Answer:
The x-axis is closer to B.
Step-by-step explanation:
Since the ratio PB:AB = 2/7 is positive, the line divides internally. So, we use the equation for the coordinates of a point that internally divide a line.
So, x = (mx₂ + nx₁)/(m + n) and y = (my₂ + ny₁)/(m + n)
where PB/AB = 2/7 = n/m. So, n = 2 and m = 7
Also, Point A = (0,0) = (x₁, y₁) and point P = (10, -5) = (x₂, y₂).
Substituting these values into x and y, we have
x = (mx₂ + nx₁)/(m + n)
x = (7(10) + 2(0)₁)/(7 + 2)
x = (70 + 0)/9
x = 70/9
x = 7⁷/₉
y = (my₂ + ny₁)/(m + n)
y = (7(-5) + 2(0)₁)/(7 + 2)
y = (-35 + 0)/9
y = -35/9
y = -3⁸/₉
So, the x and y coordinates of B are 7⁷/₉ and -3⁸/₉ respectively. So, point B is -3⁸/₉ units away from the x-axis and 7⁷/₉ units away from the y-axis. So the x-axis is closer to B.
