Question

A straight line L with negative slope passes through the points (8, 2) and cuts the positive coordinate axes at points P and Q. As L varies the absolute minimum value of OP + OQ is

(O is origin)–

• A. 28
• B. 15
• C. 18
• D. 10

Answer 1

Answer: (C)

18

Answer 2

Let the equation of the line L be

y – 2 = m (x – 8), m < 0

coordinates of P and Q are P

and Q (0, 2 – 8m)

So OP + OQ = + 2 – 8m

= 10 ++ 8(–m)

³ 10 + 2 ³ 18

absolute min. value of OP + OQ = 18.