Question

lf the distance between two given points is $2$ units and the points are transferred by shifting the origin to $(2,2)$, then the distance between the points in their new position is.

• A. $2$
• B. $5$
• C. $6$
• D. $7$

Answer 1

Answer: (A)

$2$

Shifting the origin to $(2,2)$ transforms the coordinates to
$(x,y)$ to $(x-2,y-2)$.

$\therefore$ distance between two points is

$\sqrt{(x_1-x_2{)}^2+(y_1-y_2{)}^2}$

$={\sqrt{\left(\right(x_1-2)-(x_2-2){)}^2+((y_1-2)-(y_2-2))}}^2$

$={\sqrt{(x_1-x_2{)}^2+(y_1-y_2)}}^2$

$\therefore$ distance is unaltered $=2$ units.