Question
Find the distance between the points:
$A(-6, -4)$ and $B(9, -12)$
$A(-6, -4)$ and $B(9, -12)$
✓
Answer
The given points are $A(-6, -4)$ and $B(9, -12)$
Then, $(x_1 = -6, y_1 = -4)$ and $(x_2 = 9$ and $y_2 = -12)$
$\therefore\text{AB}=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
$=\sqrt{(\text{6}+\text{9})^2+(-\text{12}+\text{4})^2}$
$=\sqrt{(\text{15})^2+(-\text{8})^2}$
$=\sqrt{\text{225}+\text{64}}$
$=\sqrt{\text{289}}=17\text{ units}.$
Then, $(x_1 = -6, y_1 = -4)$ and $(x_2 = 9$ and $y_2 = -12)$
$\therefore\text{AB}=\sqrt{(\text{x}_2-\text{x}_1)^2+(\text{y}_2-\text{y}_1)^2}$
$=\sqrt{(\text{6}+\text{9})^2+(-\text{12}+\text{4})^2}$
$=\sqrt{(\text{15})^2+(-\text{8})^2}$
$=\sqrt{\text{225}+\text{64}}$
$=\sqrt{\text{289}}=17\text{ units}.$
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