Question

If the distance between (x,3),(4,5) is 2root5 then x=

Answer 1

Given :-

• If the distance between (x,3),(4,5) is 2√5

To find :-

• Value of x

Solution :-

According to distance formula

→ AB = √(x2 - x1)² + (y2 - y1)²

Let,

• A = (x, 3)
• B = (4, 5)

According to the given condition

• AB = 2√5

→ AB = √(x2 - x1)² + (y2 - y1)²

→ 2√5 = √(4 - x)² + (5 - 3)²

→ 2√5 = √16 + x² - 8x + (2)²

→ 2√5 = √16 + x² - 8x + 4

→ 2√5 = √20 + x² - 8x

Squaring both side

→ 20 = 20 + x² - 8x

→ x² - 8x + 20 - 20 = 0

→ x² - 8x = 0

→ x(x - 8) = 0

Either

→ x = 0

Or

→ x - 8 = 0

→ x = 8

Hence,

• Value of x is 8