Question

Find the ratio AP/PB for 100 points ASAP

Answer 1

`(1)/(2)`

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 = √((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 = √((1 -(-5))^2 + (4 - 6)^2)`

`AP = √((6)^2 + (-2)^2)`

`AP = √(36 + 4) = √(40)`

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

`PB = √((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 = √((13 - 1)^2 + (0 - 4)^2)`

`PB = √((12)^2 + (-4)^2)`

`PB = √(144 + 16) = √(160)`

`(AP)/(PB) = (√(40))/(√(160))`

`= (√(40))/(2√(40))`

`= (1)/(2)`