If the distance between the points (2, -2) and (-1, x) is 5, one of the values of x is

asked Jun 13, 2022 47.2k views

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We know

$\boxed{\sf Distance=√((x_2-x_1)^2+(y_2-y_1)^2)}$

ATQ

$\\ \sf\longmapsto √((-1-2)^2+(x+2)^2)=5$

$\\ \sf\longmapsto √((-3)^2+x^2+4x+4)=5$

$\\ \sf\longmapsto √(9+x^2+4x+4)=5$

$\\ \sf\longmapsto √(x^2+4x+13)=5$

$\\ \sf\longmapsto x^2+4x+13=5^2=25$

$\\ \sf\longmapsto x^2+4x+13-25=0$

$\\ \sf\longmapsto x^2+4x-12=0$

$\\ \sf\longmapsto x^2+6x-2x-12=0$

$\\ \sf\longmapsto x(x+6)-2(x+6)=0$

$\\ \sf\longmapsto (x-2)(x+6)=0$

$\\ \sf\longmapsto x=2\:or\:x=-6$

Casbby answered Jun 20, 2022

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