Question

if the distance between the points(2,-2)and(-1,x)is 5 units then find the value of x.​

Answer 1

Answer:

two values of x

x= -4 and x=2

Step-by-step explanation:

by the formula,

D = √[(x2 - x1)² + (y2 - y1)²]

5 = √[(-2-2)² + (x-(-1))²]

5 = √(16 + (x+1)²)

squaring both sides,

5² = 16 + (x+1)²

25-16 = x² + 2x +1

9 = x² + 2x +1

x² + 2x -8 =0

x² + 4x-2x -8=0

x(x+4) -2(x+4) =0

(x+4)(x-2)=0

x = -4 or x = 2

verification,

√(16+ (2+1)²) = √(16+9) =√25 = 5 units

also,

√(16+ (-4+1)²) = √(16+9) =√25 = 5 units