Question

Match the following points to the distances between them.

• A. $2\sqrt{2}$ units
• B. $2$ units
• C. $3$ units
• D. $3\sqrt{2}$ units

Answer 1

Applying the distance formula to $(0,0),(3,3)$
$\sqrt{{(3-0)}^2+{(3-0)}^2}=\sqrt{9+9}=\sqrt{18}=3\sqrt{2}$

Applying the distance formula to $(1,1),(-1,-1)$
$\sqrt{{(-1-1)}^2+{(-1-1)}^2}=\sqrt{2^2+2^2}=2\sqrt{2}$

$(3,2),(3,5)$ have the same $x$ coordinates and hence, the distance between the $y$ coordinates of the two points which is $|2-5|=3$ units

$(3,7),(1,7)$ have the same $y$ coordinates and hence, the distance between the $x$ coordinates of the two points which is $|3-1|=2$ units