Question
Find the distance between the points:
$A(1, -3)$ and $B(4, -6)$
$A(1, -3)$ and $B(4, -6)$
✓
Answer
The given points are $A(1, -3)$ and $B(4, -6)$
Then, $(x_1 = 1, y_1 = -3)$ and ($x_2 = 4$ and $y_2 = -6)$
$\therefore\text{AB}=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
$=\sqrt{(\text{4}-\text{1})^2+(-\text{6}+\text{3})^2}$
$=\sqrt{(\text{3})^2+(-\text{3})^2}$
$=\sqrt{\text{9}+\text{9}}$
$=\sqrt{\text{18}}=3\sqrt{2}\text{ units}.$
Then, $(x_1 = 1, y_1 = -3)$ and ($x_2 = 4$ and $y_2 = -6)$
$\therefore\text{AB}=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
$=\sqrt{(\text{4}-\text{1})^2+(-\text{6}+\text{3})^2}$
$=\sqrt{(\text{3})^2+(-\text{3})^2}$
$=\sqrt{\text{9}+\text{9}}$
$=\sqrt{\text{18}}=3\sqrt{2}\text{ units}.$
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