Question

Q1.If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is *
(a) -7 or -1
O (b) -7 or 1
O (c) 7 or 1
(d) 7 or -1​

Answer 1

Answer:

d. 7 or -1

Step-by-step explanation:

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

$\sqrt{( 2 + 1) ^{2} + (3 - x) ^{2} } = 5$

(3-x)² = 25-9

(3-x)² = 16

3-x = +4

3-x = -4

x = 7,-1

Answer 2

Step-by-step explanation:

Given: The distance b/w the two given points (x, – 1) and (3, 2) is 5.

Need to find: The value of x?

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✇ To find out distance b/w any two points the require formula is Given by —

$\star\:\underline{\boxed{\pmb{\sf{Distance = \sqrt{\bigg(x_2 - x_1\bigg)^2 + \bigg(y_2 - y_1\bigg)^2}}}}}⋆$

where,

x₁ = x

x₂ = 3

y₁ = – 1

y₂ = 2

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$\begin{gathered}\underline{\bf{\dag} \:\mathfrak{Putting\;these\;values\;in\;formula :}}\\\\:\implies\sf \sqrt{\Big(x - 3\Big)^2 + \Big(-1 - 2\Big)^2} = 5 \\\\\\:\implies\sf \sqrt{\Big(x - 3\Big)^2 + 3^2} = 5^2\\\\\\:\implies\sf \Big(x - 3\Big)^2 + 9 = 5^2\\\\\\:\implies\sf x^2 - 6x + 18 = 25\\\\\\:\implies\sf x^2 - 6x = 25 - 18\\\\\\:\implies\sf x^2 - 6x -7 = 0 \\\\\\:\implies\sf x^2 - 7x + x - 7 = 0\\\\\\:\implies\sf x(x - 7) +1(x - 7) = 0\\\\\\:\implies\underline{\boxed{\pmb{\frak{x = 7\;\&\;-1}}}}\;\bigstar\end{gathered}$

⠀

$\begin{gathered}\therefore\:{\underline{\sf{Hence\;the\; value\;of\:x\;is\; {\textsf{\textbf{Option d) 7 or -1}}}.}}}\\\end{gathered}$

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$\begin{gathered}\quad\qquad\boxed{\underline{\underline{\bigstar \: \bf\:More \;to\;know\:\bigstar}}}\\\end{gathered}$

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¤ Another formula to calculate the co–ordintes of the point dividing the line segment joining two points (x₁, x₂ ) and (y₁, y₂) in the ratio of m₁ : m₂ is Section formula. It is given as:

$\Bigg(\sf\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\;\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\Bigg)$