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ehidna [41]
3 years ago
12

Given (21,7) and (x, 1), find all x such that the distance between these two points is 17.

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
6 0

Answer:

21+/-sqrt(253)=x

So one value for x is 21+sqrt(253)

and another is 21-sqrt(253)

Problem:

Given (21,7) and (x,1), find all x such that the distance between these two points is 17.

Step-by-step explanation:

Change in x is x-21

Change in y is 7-1=6

distance^2=(change in x)^2+(change in y)^2

17^2=(x-21)^2+(6)^2

289=(x-21)^2+36

Subtract 36 on both sides:

289-36=(x-21)^2

253=(x-21)^2

Take square root of both sides:

+/-sqrt(253)=x-21

Add 21 on both sides:

21+/-sqrt(253)=x

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Because of the relatively large coefficients {9, 42, 49}, applying the quadratic formula would be a bit messy. Instead, I've chosen to "complete the square:"


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