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ololo11 [35]
3 years ago
14

Find all of the points of the form (x −1) which are 4 unit from the point (3,2)

Mathematics
1 answer:
Bond [772]3 years ago
4 0

Answer:

(3+2\sqrt{2},2+2\sqrt{2}),(3-2\sqrt{2},2-2\sqrt{2})

Step-by-step explanation:

Points\ are\ of\ the\ form\ (x,x-1)\\\\Distance\ of\ these\ points\ from\ (3,2)=4\\\\\sqrt{(x-3)^2+(x-3)^2}=4\\\\\sqrt{(x-3)^2+(x-1-2)^2}=4\\\\\sqrt{2(x-3)^2}=4\\\\2(x-3)^2=16\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ square\ both\ the\ sides\\\\(x-3)^2=\frac{16}{2}\\\\(x-3)^2=8\\\\(x-3)=\pm 2\sqrt{2}\ \ \ \ \ \ \ \ \ \ \ square\ root\ both\ the\ sides\\\\x=3\pm 2\sqrt{2}\\\\When\ x=3+2\sqrt{2}\ \ \Rightarrow x-1=3+2\sqrt{2}-1=2+2\sqrt{2}\\\\When\ x=3-2\sqrt{2}\ \ \Rightarrow x-1=3-2\sqrt{2}-1=2-2\sqrt{2}

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