Answer:
x =5
Step-by-step explanation:
Using the formula for calculating the distance between two points
D = √(x2-x1)²+(y2-y1)²
Given the points A(2, x) , B(x, 8) and AB = 3√2
On substituting the given values into the formula;
AB = √(x-2)²+(8-x)²
3√2= √(x-2)²+(8-x)²
square both sides
(3√2)²= (x-2)²+(8-x)²
18 = (x-2)²+(8-x)²
expand
18 = x²-4x+4+64-16x+x²
18 = 2x²-20x+68
2x²-20x+68-18 = 0
2x²-20x+50 = 0
x²-10x+25 = 0
Factorize
x²-5x-5x+16 = 0
x(x-5)-5(x-5) = 0
(x-5)(x-5) = 0
x-5 = 0 an x-5 = 0
x = 5
