Question

6. Find the distance between points (3, 3) and (3,-7)
(A) 100
(B) 10
(C) -100
(D) -10​

Answer 1

$\Huge{\textbf{\textsf{{\purple{Ans}}{\pink{wer}}{\color{pink}{:}}}}}$

$the \: distance \: between \: points \: (3, 3) \: \\ and \: (3,-7) \: is \: \\ \sqrt{ {(3 - 3)}^{2} + {(3 + 7)}^{2} } \\ = \sqrt{ {0}^{2} + {10}^{2} } \\ = 10$

so option B) 10 is the correct answer

Answer 2

Given: We've provided two points (3, 3) and (3, –7).

Need to find: The Distance b/w the points.

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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 = 3
• x₂ = 3
• y₁ = 3
• y₂ = –7

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{Putting\;these\;values\;in\;formula :}}$⠀⠀⠀

$:\implies\sf Distance = \sqrt{\bigg(x_2 - x_1\bigg)^2+\bigg(y_2 - y_1\bigg)^2}$

$:\implies\sf Distance = \sqrt{\bigg(3 - 3\bigg)^2+\bigg(-7 - 3\bigg)^2}$

$:\implies\sf Distance = \sqrt{\bigg(0^2 + 10^2\bigg)}$

$:\implies\sf Distance = \sqrt{100}$

$:\implies{\pmb{\sf{Distance = 10}}}$

$\therefore\:{\underline{\sf{Hence\;the\; Distance\;b/w\; points\;is\; {\textsf{\textbf{Option b) 10}}}.}}}$⠀

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$\quad\qquad\boxed{\underline{\underline{\bigstar \: \bf\:More \;to\;know\:\bigstar}}}$⠀⠀⠀

¤ 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:

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