Question

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

Answer 1

Given Points

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

Using Formula

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

Substuting the values

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

`\bf \longrightarrow \: Distance \: = \: \sqrt{ (1) ^(2) \: + \: (1 \: + \: 7 ) ^(2) }`

`\bf \longrightarrow \: Distance \: = \: \sqrt{ 1 \: + \: (8 ) ^(2) }`

`\bf \longrightarrow \: Distance \: = \: √( 65 )`

`\Large \purple \diamond \: \: \underbrace {\rm {{{\color{blue}{Distance \: = \: √(65) }}}}} \: \: \purple \diamond`

Answer 2

sqrt(65)

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)