Question

find the distance between the points (2,5)and (6,1)

Answer 1

distance between joining of A(x1,y1) and B(x2,y2) =√(x2-x1)²+(y2-y1)²

let A(x1,y1) =(2,5)
B (x2,y2) =(6,1)
AB =√(6-2)²+(1-5)²

= √4²+(-4)²
=√16+16
=√32
=√(4*4)*2
=4√2

Answer 2

$\huge \underline \mathfrak {Solution:-}$

We have to find out the distance between the two points (2,5) and (6,1).

For finding the distance between two points we can use the given formula.

Distance $= \sqrt{ {(x_1 - x_2)}^{2} + {(y_1 - y_2)}^{2} }$

This formula is used to find out the distance between two points and that's why it is named as distance formula.

According to question,

$x_1 = 2 \\ \\ x_2 = 6 \\ \\ y_1 = 5\\ \\ y_2 = 1$

Now,

Distance $= \sqrt{ {(x_1 - x_2)}^{2} + {(y_1 - y_2)}^{2} }$

$= \sqrt{ {(2-6)}^{2} + {( 5-1)}^{2} } \\ \\ = \sqrt{ {( -4)}^{2} + { (4)}^{2} } \\ \\ = \sqrt{ {4}^{2} + {4}^{2} } \\ \\ = \sqrt{ {4}^{2}(1 + 1) } \\ \\ = 4 \sqrt{2} \: units$

So, the distance between the points is 4√2 units.