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Partha, a software engineer, lives in Jerusalem for his work. He lives in the most convenient area of the city from where bank, hospital, post office and supermarket can be easily accessed. In the graph, the bank is plotted as A$(9, 5)$, hospital as B$(-3,-1)$ and supermarket as C$(5,-5)$ such that A, B, C form a triangle.
Based on the above given information, answer the following questions :
(i) Find the distance between the bank and the hospital.
(ii) In between the bank and the supermarket, there is a post office plotted at E which is their mid-point. Find the coordinates of E.
(iii) (a) In between the hospital and the supermarket, there is a bus stop plotted as D, which is their mid-point. If Partha wants to reach the bus stand from the bank, then how much distance does he need to cover ?
OR
(b) P and Q are two different garment shops lying between the bank and the hospital, such that BP = PQ = QA. If the coordinates of P and Q are $(1, a)$ and $(b, 3)$ respectively, then find the values of 'a' and 'b'.
Based on the above given information, answer the following questions :
(i) Find the distance between the bank and the hospital.
(ii) In between the bank and the supermarket, there is a post office plotted at E which is their mid-point. Find the coordinates of E.
(iii) (a) In between the hospital and the supermarket, there is a bus stop plotted as D, which is their mid-point. If Partha wants to reach the bus stand from the bank, then how much distance does he need to cover ?
OR
(b) P and Q are two different garment shops lying between the bank and the hospital, such that BP = PQ = QA. If the coordinates of P and Q are $(1, a)$ and $(b, 3)$ respectively, then find the values of 'a' and 'b'.
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(i) Distance between bank and hospital $= \sqrt{(-3-9)^2 + (-1 - 5)^2}$
$= \sqrt{180}$ units or $6\sqrt{5}$ units
(ii) Coordinates of E are $(\frac{9+5}{2}, \frac{5+(-5)}{2}) = (7,0)$
(iii) (a) Coordinates of D are $(\frac{-3+5}{2}, \frac{-1+(-5)}{2}) = (1, -3)$
Distance Partha need to cover $= \sqrt{(9-1)^2 + (5 - (-3))^2}$
$= \sqrt{128}$ units or $8\sqrt{2}$ units
OR
(iii) (b) P is mid-point of BQ
$\therefore a = \frac{-1+3}{2} = 1$
Q is mid-point of PA
$\therefore b = \frac{1+9}{2} = 5$
$= \sqrt{180}$ units or $6\sqrt{5}$ units
(ii) Coordinates of E are $(\frac{9+5}{2}, \frac{5+(-5)}{2}) = (7,0)$
(iii) (a) Coordinates of D are $(\frac{-3+5}{2}, \frac{-1+(-5)}{2}) = (1, -3)$
Distance Partha need to cover $= \sqrt{(9-1)^2 + (5 - (-3))^2}$
$= \sqrt{128}$ units or $8\sqrt{2}$ units
OR
(iii) (b) P is mid-point of BQ
$\therefore a = \frac{-1+3}{2} = 1$
Q is mid-point of PA
$\therefore b = \frac{1+9}{2} = 5$