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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Solution

Q.
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 question :

Q. 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’.

Ans.
(a = 1, b = 5)

P is mid-point of BQ

$∴$ $a = \frac{- 1 + 3}{2} = 1$

Q is mid-point of PA

$∴$ $b = \frac{1 + 9}{2} = 5$

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