| Find the distance between the points\[A\,\,(-\,\,6,8)\]and \[B\,\,(4,-8).\] |
A) 18.86 units
B) 19 units
C) 22 units
D) 25.25 units
Correct Answer: A
Solution :
| Here, \[A\,\,(-\,\,6,8)=A\,\,({{x}_{1}},{{y}_{1}})\]and |
| \[B\,\,(4,-\,\,8)=B\,\,({{x}_{2}},{{y}_{2}})\] |
| \[\therefore \]\[{{x}_{1}}=-\,\,6,\]\[{{y}_{1}}=8,\]\[{{x}_{2}}=4\]and \[{{y}_{2}}=-\,\,8\] |
| \[\therefore \]Required distance, |
| \[AB=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}\] |
| \[=\sqrt{{{(4+6)}^{2}}+{{(-16)}^{2}}}=\sqrt{100+256}\] |
| \[=\sqrt{356}=18.86\,\,\text{units}\] |
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