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Find all possible values of y for which the distance between t

Question

Find all possible values of y for which the distance between the points $A (2, - 3)$ and $B (10, y)$ is $10$ units.

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Find all possible values of y for which the distance between the points

A (2, - 3)

and

B (10, y)

10

units.

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

Given: Points

A (2, - 3), B (10, y)

and

A B = 10

Distance formula:

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

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

(10)^{2} = (10 - 2)^{2} + (y + 3)^{2}

100 = (8)^{2} + y^{2} + 6 y + 9

y^{2} + 6 y + 9 + 64 = 100

y^{2} + 6 y + 73 - 100 = 0

y^{2} + 6 y - 27 = 0

y^{2} + 9 y - 3 y - 27 = 0

y (y + 9) - 3 (y + 9) = 0

(y + 9) (y - 3) = 0

Either,

y + 9 = 0

, then

y = - 9

y - 3 = 0

, then

y = 3

y = 3, - 9

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Question Text	Find all possible values of y for which the distance between the points $A (2, - 3)$ and $B (10, y)$ is $10$ units.
Answer Type	Text solution:1
Upvotes	150