Question

If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:
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Answer 1

AnSwEr :-

• 2 or -6.

Given :-

• The distance between the points A(2, -2) and B(-1, x) is equal to 5.

To Find :-

• Value of x

SoluTion :-

Here,

• x1 = 2
• y1 = -2
• x2 = -1
• y2 = x

Formula for finding distance between two points is :-

$\sqrt{{(x2 - x1) {}^{2} } + (y2 - y1) {}^{2} }$

Put the values in the formula :-

√ (- 1 - 2)² + {x - (-2)}² = 5

→ √ { (-3)² + (x + 2)² } = 5

→ √{ 9 + (x + 2)² } = 5

→ 9 + (x + 2)² = 25

→ (x + 2)² = 16

→ x + 2 = ± 4

_____________________

• x + 2 = 4

→ x = 4 - 2

→ x = 2

_____________________

• x + 2 = - 4

→ x = - 4 - 2

→ x = - 6

Hence, the value of x is 2 or -6.

__________________________

Answer 2

Given :  the distance between the points A(2, -2) and B(-1, x) is equal to 5,

To Find : value of x  

Solution:

Distance between two points ( a , b) and (c , d)  is given by

= √(c - a)² + (d - b)²

points A(2, -2) and B(-1, x) √(-1 - 2)² + ( x - (-2))²

=> Distance = √(-1 - 2)² + ( x = (-2))²

=> Distance = √(-3)² + ( x +2)²

Distance = 5

=> 5 = √(-3)² + ( x +2)²

Squaring both sides

=> 25 = 9  + (x + 2)²

=> 16 = (x + 2)²

=> x + 2 = ± 4

=> x = -6  or  2

Value of x is 2 or - 6

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