Question

# Find the distance between the given points: (i) A (3, -4), B (-5,6)

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Solution

## The given points are A(3, –4), B(–5, 6). From these points, x1 = 3, y1 = –4, x2 = –5, y2 = 6. By the distance formula, $\mathrm{AB}=\sqrt{\left({x}_{2}-{x}_{1}{\right)}^{2}+\left({y}_{2}-{y}_{1}{\right)}^{2}}\phantom{\rule{0ex}{0ex}}=\sqrt{\left(-5-3{\right)}^{2}+\left[6-\left(-4\right){\right]}^{2}}\phantom{\rule{0ex}{0ex}}=\sqrt{\left(-8{\right)}^{2}+\left(10{\right)}^{2}}\phantom{\rule{0ex}{0ex}}=\sqrt{64+100}\phantom{\rule{0ex}{0ex}}=\sqrt{164}\phantom{\rule{0ex}{0ex}}=2\sqrt{41}$

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