Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively.

Question

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:

Accepted Answer

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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