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Nostrana [21]
3 years ago
12

Find the distance between (3, −7) and (4, 1). Write your answer using a radical sign.

Mathematics
2 answers:
mr_godi [17]3 years ago
6 0
<h2><u>Given Points</u></h2>

  • ( 3 , -7 ) x = 3 and y = -7
  • ( 4 , 1 ) x = 4 and y= 1

<h2><u>Using</u><u> Formula</u></h2>

\large\begin{gathered} {\underbrace{\boxed{ \bf {\red{Distance \:  =  \:  \sqrt{(x_2 \:  -  \: x_1) ^{2}  \:  +  \: (y_2 \:  -  \: y_1) ^{2} } }}}}}\end{gathered}

<h2><u>Substuting</u><u> the</u><u> values</u></h2>

<u>\bf \longrightarrow \: Distance \:  =  \:  \sqrt{ \bigg(4 \:  -  \: 3 \bigg) ^{2}  \:  +  \:  \bigg(1 \:  -  \: [ - 7 ]\bigg) ^{2} }</u>

<u>\bf \longrightarrow \: Distance \:  =  \:  \sqrt{ (1) ^{2}  \:  +  \:  (1 \:   +  \: 7 ) ^{2} }</u>

<u>\bf \longrightarrow \: Distance \:  =  \:  \sqrt{ 1  \:  +  \:  (8 ) ^{2} }</u>

<u>\bf \longrightarrow \: Distance \:  =  \:  \sqrt{ 65 }</u>

<u>\Large  \purple \diamond \:  \:    \underbrace {\rm {{{\color{blue}{Distance \:  =  \:  \sqrt{65} }}}}} \:  \:  \purple   \diamond</u>

AlladinOne [14]3 years ago
5 0

Answer:

sqrt(65)

Step-by-step explanation:

To find the distance between the two points

d = sqrt(  (x2-x1)^2+ (y2-y1)^2)

   = sqrt( (4-3)^2 +(1 - -7)^2)

    = sqrt( 1^2 + (1+7)^2)

    = sqrt( 1+8^2)

    = sqrt(1+64)

sqrt(65)

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