Question

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

Answer 1

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`