Question

The distance between the points $(x_1,-y_1)\text{and}(-x_2,y_2)$ is ___ units.

• A. $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
• B. $\sqrt{(x_2+x_1{)}^2+(y_2-y_1{)}^2}$
• C. $\sqrt{(x_2-x_1{)}^2+(-y_2-y_1{)}^2}$
• D. $\sqrt{(x_2+x_1{)}^2+(y_2+y_1{)}^2}$

Answer 1

The correct option is D $\sqrt{(x_2+x_1{)}^2+(y_2+y_1{)}^2}$

The distance between two points $(x_1,y_1)and(x_2,y_2)$ is given by
$\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

Thus, the distance between
$(x_1,-y_1)and(-x_2,y_2)$ will be
$\sqrt{(-x_2-x_1{)}^2+(y_2-(-y_1){)}^2}$
$=\sqrt{(x_2+x_1{)}^2+(y_2+y_1{)}^2}\because (-x_2-x_1{)}^2=(x_2+x_1{)}^2$