Answer :
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)
Given Points
- ( 3 , -7 ) x = 3 and y = -7
- ( 4 , 1 ) x = 4 and y= 1
Using Formula
[tex] \large\begin{gathered} {\underbrace{\boxed{ \bf {\red{Distance \: = \: \sqrt{(x_2 \: - \: x_1) ^{2} \: + \: (y_2 \: - \: y_1) ^{2} } }}}}}\end{gathered}[/tex]
Substuting the values
[tex] \bf \longrightarrow \: Distance \: = \: \sqrt{ \bigg(4 \: - \: 3 \bigg) ^{2} \: + \: \bigg(1 \: - \: [ - 7 ]\bigg) ^{2} }[/tex]
[tex] \bf \longrightarrow \: Distance \: = \: \sqrt{ (1) ^{2} \: + \: (1 \: + \: 7 ) ^{2} }[/tex]
[tex] \bf \longrightarrow \: Distance \: = \: \sqrt{ 1 \: + \: (8 ) ^{2} }[/tex]
[tex] \bf \longrightarrow \: Distance \: = \: \sqrt{ 65 }[/tex]
[tex]\Large \purple \diamond \: \: \underbrace {\rm {{{\color{blue}{Distance \: = \: \sqrt{65} }}}}} \: \: \purple \diamond[/tex]