Question

Find the distance between the points $(-1,6)$ and $(2,2).$

• A. $\text{3 units}$
• B. $\text{4 units}$
• C. $\text{5 units}$
• D. $\text{6 units}$

Answer 1

The correct option is C $\text{5 units}$

We know that, distance between the points $(x_1,y_1)$ and $(x_2,y_2)$
$=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$\therefore$ Distance between the points $(-1,6)$ and $(2,2)$
$=\sqrt{(2-(-1){)}^2+(2-6{)}^2}$
$=\sqrt{(2+1{)}^2+(-4{)}^2}$
$=\sqrt{3^2+(-1{)}^2\times 4^2}$
$=\sqrt{3^2+1\times 4^2}$
$=\sqrt{3^2+4^2}$
$=\sqrt{9+16}(\because 3^2=3\times 3=9,4^2=4\times 4=16)$
$=\sqrt{25}$
$=\sqrt{5\times 5}$
$=\sqrt{5^2}$
$=5(\because \text{Square root and the square cancel each other out.})$

Hence, option(c.) is the correct choice.