Final answer:
To find the value of p such that AP is two-sevenths of PB, we need to find the coordinates of the points A and B and then use the distance formula and proportion to solve for p.
Step-by-step explanation:
To find the value of p such that AP is two-sevenths of PB, we need to find the coordinates of the points A and B and then use the distance formula and proportion to solve for p.
The coordinates of A are (-5,8) and the coordinates of B are (9,3). Using the distance formula, we can find the distance between A and B as:
d = sqrt((9 - (-5))^2 + (3 - 8)^2) = sqrt(196 + 25) = sqrt(221).
Since AP is two-sevenths of PB, we have:
(2/7)(sqrt(221)) = (5 - p)/(p - (-5)).
Solving this equation for p will give us the desired value.