Question

if the distance between the two points (8,x) and (x,8 ) is 2root2 units then find value of x

Answer 1

distance between (8,x) and (x,8) = √((8-x)² + (x-8)²) = 2√2
solving for x
√(x-8)² = 2
x-8 = ±2
x=6 or 10

Answer 2

Answer:

The value of x is 6 or 10. So, the two points are (8,10) and (10,8) or (8,6) and (6,8).

Step-by-step explanation:

Given, the two points are (8,x) and (x,8)

The distance between two points is 2√2.

Using, Euclidean distance formula, we get

$\sqrt{(8-x)^2 + (x-8)^2} = 2\sqrt{2}$

⇒ (8-x)² + (x-8)² = 8

⇒ 64 + x² -16x + 64 + x² - 16x = 8

⇒ 2(x² -16x + 64) = 8

⇒ x² -16x + 64 = 4

⇒ x² -16x + 60 = 0

⇒ x² -10x - 6x + 60 = 0

⇒ x(x-10) -6(x-10) = 0

⇒ (x-10)(x-6) = 0

⇒ x = 10 or x = 6

Hence, the two points are (8,10) and (10,8) or (8,6) and (6,8).

To learn more about Euclidean distance, click on the link below:

https://brainly.in/question/54286865

To learn more about two points, click on the link below:

https://brainly.in/question/5971539

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