Question

Find x so the distance between the points (x,2) and (-1,-2) is
`2√(5)`

x =_____ , ______

Answer 1

x = -5 , 3

Explanation:

(x₁ , y₁) = (-1, -2) & (x₂, y₂) = (x , 2)

`Distance =\sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)}\\\\\\\sqrt{(x - [-1])^(2)+(2-[-2])^(2)}=2√(5)\\\\\sqrt{(x+1)^(2)+(2+2)^(2)}=2√(5)\\\\\sqrt{(x)^(2)+2x+1+(4)^(2)}=2√(5)\\\\\sqrt{x^(2)+2x+1+4}=2√(5)\\\\\sqrt{x^(2)+2x+5}=2√(5)`

Take square both sides,

x² + 2x + 5 = (2)²(√5)² {(√5)² = √5*√5 = 5 }

x² + 2x +5 = 4 * 5

x² + 2x + 5 = 20

x² + 2x + 5 - 20 = 0

x² + 2x -15 = 0

x² + 5x - 3x - 5*3 = 0

x(x + 5) -3(x + 5)=0

(x + 5)(x - 3) = 0

x + 5 = 0 ; x - 3 = 0

x = -5 ; x = 3

x = -5 , 3