Question

Find the value of x for which the distance between the points A ( x,-3 ) and B ( -4 ,2) is 5√5 units

Answer 1

Answer:14 or 6

Step-by-step explanation:

Answer 2

Answer:

The value of x is 6.

Step-by-step explanation:

• If two points are given like $(x_1,y_1) and (x_2,y_2)$, then the distance between two points is calculated by the following formula:      Distance = $\sqrt{(y_2-y_1)^2 + (x_2-x_1)^2}$
• Solution: Two points are A and B. A = ( x,-3 ) and B = ( -4 ,2)

       The distance between them = AB = $\sqrt{(2+3)^2 + (-4-x)^2}$

                                                                 = $\sqrt{25 + (-4-x)^2}$

  The given condition is AB = 5√5

  So we can write,  $\sqrt{25 + (-4-x)^2}$ = 5√5

                               ${25 + (-4-x)^2} = (5\sqrt{5} )^2$  [taking square on both sides]

                                (x + 4)² = 125 - 25 = 100 = 10²

                                 x + 4 = 10

                                 x = 10 - 4 = 6

   ∴ The value of x is 6.

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