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Find the values of x for which the distance between the points

Question

Find the values of x for which the distance between the points $P (x, 4)$ and $Q (9, 10)$ is $10$ units.

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Find the values of x for which the distance between the points

P (x, 4)

and

Q (9, 10)

10

units.

15 mins ago

Discuss this question LIVE

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Text solutionVerified

Given: Points

P (x, 4), Q (9, 10)

and

PQ = 10

Distance formula:

PQ = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

P Q^{2} = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

100 = (9 - x)^{2} + (10 - 4)^{2}

= 81 + x^{2} - 18 x + 36

= 117 + x^{2} - 18 x

100 = 117 + x^{2} - 18 x

x^{2} - 18 x + 17 x = 0

(solve this equation)

(x - 1) (x - 17)

x = 1

x = 17

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Question Text	Find the values of x for which the distance between the points $P (x, 4)$ and $Q (9, 10)$ is $10$ units.
Answer Type	Text solution:1
Upvotes	152