Question

The point A(2, 1) is translated parallel to the line x – y = 3 by 4 units. If the new point lies in the third quadrant, then the coordinates of the new point are-

• A. $\left( \frac { 2 } { 3 } , \frac { - 1 } { 3 } \right)$
• B. $\left( \frac { 1 } { 2 } , \frac { - 1 } { 2 } \right)$
• C. $( - \sqrt { 2 } + 1 , - \sqrt { 2 } )$
• D. $( 2 - 2 \sqrt { 2 } , 1 - 2 \sqrt { 2 } )$

Answer 1

Answer: (D)

$( 2 - 2 \sqrt { 2 } , 1 - 2 \sqrt { 2 } )$

Answer 2

Slope of AB = 1

i.e. = 1

i.e. h – k = 1

and AB = 4

i.e. (h – 2)² + (k – 1)² = 16

i.e. (k – 1)² + (k – 1)² = 16

given k = 1 – $\sqrt { 8 }$

andh = 2 – $\sqrt { 8 }$ is not acceptable

Q B lies in the third quadrant]