Question
Find the distance between the points:
$A(7, -4)$ and $B(-5, 1)$
$A(7, -4)$ and $B(-5, 1)$
✓
Answer
The given points are $A(7, 4)$ and $B(-5, 1)$
Then, $(x_1 = 7, y_1 = -4)$ and ($x_2 = -5$ and $y_2 = 1$)
$\therefore\text{AB}=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
$=\sqrt{(-\text{5}-\text{7})^2+(\text{1}+\text{4})^2}$
$=\sqrt{(-\text{12})^2+(\text{5})^2}$
$=\sqrt{\text{144}+\text{25}}$
$=\sqrt{\text{169}}=13\text{ units}.$
Then, $(x_1 = 7, y_1 = -4)$ and ($x_2 = -5$ and $y_2 = 1$)
$\therefore\text{AB}=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
$=\sqrt{(-\text{5}-\text{7})^2+(\text{1}+\text{4})^2}$
$=\sqrt{(-\text{12})^2+(\text{5})^2}$
$=\sqrt{\text{144}+\text{25}}$
$=\sqrt{\text{169}}=13\text{ units}.$
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