Question

2.

Find the value of 'x' if the distance between (x, 2) and (3, 4) is 8 units.​

Answer 1

❏ Question

Find the value of 'x' if the distance between (x, 2) and (3, 4) is 8 units.

❏Answer

GIVEN:-

• the distance between (x, 2) and (3, 4) is 8 units.

FIND:-

• Value of x .

❏Explanation:-

( We know )

if given any two points A(a,b) and B(c,d) ,then Distance between these point

[ AB = √{(a-c)²+(b-d)²}. ]

Now,

Distance between (x,2) and (3,4) will be

= √{ (x-3)²+(2-4)²}

➥ 8 = √{(x-3)²+(-2)²}

➥ 8 = √{(x-3)²+4}

(Squaring both side )

➥(x-3)²+4 = 8²

Using identity

★ (a+b)² = a² + b² + 2ab

➥ x²+9-6x+4-64=0

➥ x² - 6x - 51 = 0

➥ x² - 13x + 7x -51 =0

➥ x (x -13 ) +7 ( x - 13) =0

➥ ( x-13)(x+7) = 0

➥ (x-13) = 0. Or. ( x +7 ) =0

➥ x = 13 or. x = -7. [ Ans ]

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