Question

IfA(5,8), B (1,4) and C (x, 2) then find the value of x.​

Answer 1

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$\huge \boxed{ \fcolorbox{purple}{pink}{answer}} \\ \: \\ ac = \sqrt{ {(x - 5)}^{2} + {(2 - 8)}^{2} } \\ ac = \sqrt{ {x}^{2} + 25 - 10x + 36} \\ ac = \sqrt{ {x}^{2} - 10x + 61 } \\ \\ now \\ bc = \sqrt{ {(x - 1)}^{2} + {(2 - 4)}^{2} } \\ bc = \sqrt{ {x}^{2} - 2x + 5} \\ ac = bc \\ \sqrt{ {x}^{2} - 10x + 61 } = \sqrt{ {x}^{2} - 2x + 5 } \\ \\ squaring \: on \: both \: side \\ \\ {x}^{2} - 10x + 61 = {x}^{2} - 2x + 5 \\ \\ - 8x + 61 - 5 = 0 \\ \\ - 8x + 56 \\ \frac{ - 8x}{8} + \frac{56}{8} \\ x - 7 \\ x = 7$

☆we use distance formula in this question.☆

☆if c is equadistance fromA and B

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Answer 2

The value of x is equal to - 1.

Step-by-step explanation:

The given three points A(5, 8), B(1, 4) and C (x, 2) are collinear.

To find, the value of  x = ?

We know that,

The condition of three points are collinear.

$x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})=0$

⇒ 5(4 - 2) + 1(2 - 8) + x(8 - 4) = 0

⇒ 5(2) + 1(- 6) + x(4) = 0

⇒ 10 - 6 + 4x = 0

⇒ 4x + 4 = 0

⇒ 4x = - 4

⇒ x = - 1

Thus, the value of x is equal to - 1.