Question

Find the ratio AP/PB for 100 points ASAP

Answer 1

Answer:

$\frac{1}{2}$

Step-by-step explanation:

To find the ratio of AP/PB, find the distance between A and P, then P and B.

Distance between A(-5, 6) and P(1, 4):

$AP = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$A(-5, 6) = (x_1, y_1)$

$P(1, 4) = (x_2, y_2)$

$AP = \sqrt{(1 -(-5))^2 + (4 - 6)^2}$

$AP = \sqrt{(6)^2 + (-2)^2}$

$AP = \sqrt{36 + 4} = \sqrt{40}$

Distance between P(-1, 2) and B(1, -2):

$PB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$P(1, 4) = (x_1, y_1)$

$B(13, 0) = (x_2, y_2)$

$PB = \sqrt{(13 - 1)^2 + (0 - 4)^2}$

$PB = \sqrt{(12)^2 + (-4)^2}$

$PB = \sqrt{144 + 16} = \sqrt{160}$

$\frac{AP}{PB} = \frac{\sqrt{40}}{\sqrt{160}}$

$= \frac{\sqrt{40}}{2\sqrt{40}}$

$= \frac{1}{2}$