Question

Distance between the points (4,6)and (6,8) is
A) root 2Units
B) 2 Units
C) 2 root 2Units
D) 4Units​

Answer 1

$\pink{ \sf \rightarrow \: Given :-}$

$\sf \: The \: points \: \: (4 \: , \: 6) \: and(6 \: ,\: 8)$

$\red{ \sf \: \rightarrow \: To \: find:-}$

$\sf \: D istance \: between \: them \:$

$\purple{ \sf \: \rightarrow \: S olution:-}$

$\sf \: As \: we \: know \: that \: ,$

$\sf \: If \: the \: points \: (x_1,y_1) \: and \: (x_2,y_2) \: distance \: between \: them \: is \:$

$\sf{\boxed{ \pink{ \sqrt{(x_1 - x_2) {}^{2} + (y_1 - y_2) {}^{2} }}} }$

$\sf \: (x_1,y_1) = (4,6) \\ \sf \: (x_2,y_2) = (6,8)$

$\rightarrow \: \sf \: S ubstituting \: the \: values \: ,$

$\sf { = \sqrt{(4 - 6) {}^{2} + (6 - 8) {}^{2} } }$

$\sf { = \sqrt{( - 2) {}^{2} + ( - 2) {}^{2} } }$

$\sf { = \sqrt{4 + 4 } }$

$\sf { = \sqrt{8 } }$

$\sf { = 2 \sqrt{2 } units }$

$\sf S o \: the \: distance \: between \: the \: given \: points \: is \: \pink{2 \sqrt{2}units }$

Option- c

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\pink{ \sf \rightarrow \: Know \: more \: formulae \: :-}$

$\red{ \sf \: \rightarrow \: Section \: formula(Internal \: Division)}$

$\sf \: \bigg( \dfrac{mx_2 + nx_1}{m + n} , \dfrac{my_2 + ny_1}{m + n} \bigg)$

$\red{ \sf \: \rightarrow \: Section \: formula(External \: Division)}$

$\sf \: \bigg( \dfrac{mx_2 - nx_1}{m - n} ,\dfrac{my_2 - ny_1}{m - n} \bigg)$

$\red{ \sf \: \rightarrow \: Centroid \: formula}$

$\sf \bigg( \dfrac{x_1 + x_2 + x_3}{3} , \dfrac{y_1 + y_2 + y_3}{2} \bigg)$

$\red{ \sf \: \rightarrow \: Mid \: point \: \: formula}$

$\sf \bigg( \dfrac{x_1 + x_2 }{2} , \dfrac{y_1 + y_2 }{2} \bigg)$

Answer 2

Step-by-step explanation:

$\large \underline \bold \red{Question →}$

⟶ Distance between the points ( 4,6 ) and ( 6,8 ) is :-

• Root 2 units
• 2 Units
• 2 roots 2 units
• 4 units

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$\large \underline \bold \red {Answer →}$

⟹ Given :-

• The Points ( 4 , 6 ) and ( 6 , 8 )

⟹ To Find :-

• Distance between the given points.

$\large{ \underline \mathfrak\pink{Solution →}}$

⟼ Let,

• A ( 4,6 ) and B ( 6,8 ) be the points.

$\bold{Distance \: between \: two \: points} \\ \bold = { \sqrt{( x_{2} - x_{1}) {}^{2} + ( y_{2} - y_{1}) {}^{2} } }$

⟼ Now,

• Substituting the values -

$\bold{PQ = \sqrt{(6 - 4) {}^{2} + (8 - 6) {}^{2} } \: units } \\ \bold{ = \sqrt{2 {}^{2} + {2}^{2} } \: units } \\ \bold{ = \sqrt{4 + 4} \: units} \\ \bold{ = \sqrt{8} \: units } \\ \bold \pink { =2 \sqrt{2} \: units }$

⟼ Hence,

• 3 option is correct [ 2 root 2 units ].

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$\bigstar\large\underline\mathcal\pink{Learn \: More \: :- }$

1.] https://brainly.in/question/23029479

2.] https://brainly.in/question/14212628

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$\large\colorbox{pink}{Hope lt'z Help You ❥ }$