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Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point (–1, –4) in this line is :

JEE · Math · previous-year question

  1. A.$$\left( {{{11} \over 5},{{28} \over 5}} \right)$$correct
  2. B.$$\left( {{{29} \over 5},{{11} \over 5}} \right)$$
  3. C.$$\left( {{{29} \over 5},{8 \over 5}} \right)$$
  4. D.$$\left( {{8 \over 5},{{29} \over 5}} \right)$$

Answer

A. $$\left( {{{11} \over 5},{{28} \over 5}} \right)$$

Explanation

Line is $${x \over 3} + {y \over 1} = 1$$ $$ \Rightarrow $$ x + 3y – 3 = 0 Let Image of point (–1, –4) is ($$\alpha $$, $$\beta $$) Hence, $${{\alpha + 1} \over 1} = {{\beta + 4} \over 3} = - 2\left( {{{ - 1 - 12 - 3} \over {10}}} \right)$$ $$ \Rightarrow $$ $${{\alpha + 1} \over 1} = {{\beta + 4} \over 3} = {{16} \over 5}$$ $$ \Rightarrow $$ $$\alpha $$ = $${{11} \over 5}$$, $$\beta $$ = $${{28} \over 5}$$

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