Question

If the distance the points (2, -2) and (-1, x) is 5, one of the values of x is:
A) -2
B) 2
C) -1
D) 1

Answer 1

Heya!
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◾Coordinate Geometry ◾
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↪Let the Points be ->


=> A ( 2 , -2 )

=> B ( -1 , x )


⭐Distance AB = 5 units .



〰Applying Distance Formula ,



$\sqrt{(2 - ( - 1) {}^{2} + ( - 2 - x) {}^{2} } \\ \\ \\ = > \sqrt{(2 + 1) {}^{2} + (x + 2) {}^{2} } \\ \\ = > \sqrt{(3) {}^{2} + x {}^{2} + 4 + 4x } = 5 \\ \\ = > \sqrt{9 + 4 + x {}^{2} + 4x } = 5 \\ \\ = > \sqrt{13 + x {}^{2} + 4x } = 5$


↪Squaring Both Sides ->
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=> 13 + x² + 4x = 25

=> x² + 4x - 12 = 0

=> x² + 6x - 2x - 12 = 0

=> x ( x + 6 ) -2 ( x + 6 )


=> ( x - 2 ) ( x + 6 )


=> x = 2 , -6



◾◾Hence from the Given Options Option ( B ) 2 ✔ is Correct !!
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