Question

The distance between the points (2, 1) and (3, 2) is
a)2units
b)√2units
c)√5units
d)√3units​

Answer 1

Answer:

THE ANSWER IS

$\sqrt{2}$

Step-by-step explanation:

$\sqrt{ {(x2 - x1)}^{2} + ({y2 - y1}^{2}) } \\ \sqrt{ {(3 - 2)}^{2} + {(2 - 1)}^{2} } \\ \sqrt{ {(1)}^{2} + {(1)}^{2} } \\ \sqrt{1 + 1} \\ \sqrt{2}$

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Answer 2

Answer :

• Distance is √2 units

Explanation :

Use Distance formula :

$\longrightarrow \sf{|AB| \: = \: \sqrt{(x_2 \: - \: x_1)^2 \: + \: (y_2 \: - \: y_1)^2}} \\ \\ \longrightarrow \sf{|AB| \: = \: \sqrt{(3 \: - \: 2)^2 \: + \: (2 \: - \: 1)^2}} \\ \\ \longrightarrow \sf{|AB| \: = \: \sqrt{(1)^2 \: + \: (1)^2}} \\ \\ \longrightarrow \sf{|AB| \: = \: \sqrt{1 \: + \: 1}} \\ \\ \longrightarrow \sf{|AB| \: = \: \sqrt{2}} \\ \\ \underline{\underline {\sf{Distance \: between \: points \: is \: \sqrt{2} \: units}}}$

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Additional Information

• Section formula, when the line segment is in two ratio of m1:m2

$\sf{x = \dfrac{(m_1x_2 + m_2x_1)}{(m_1+m_2)}}$

And,

$\sf{y = \dfrac{(m_1y_2 + m_2y_1)}{(m_1+m_2)}}$

• Mid Point formula is $\sf{\dfrac{(x_1+x_2)}{2} and \dfrac{(y_1+y_2)}{2}}$

• The area of the triangle formed by the points $\sf{(x_1,y_1)(x_2,y_2) and (x_3,y_3)}$ is the numerical value of the expression:

$\sf\dfrac{1}{2}[x_1(y_2-y_3)+x_2 (y_3-y_1)+x_3(y_1-y_2)]$