Question

What is the distance between the points (5, 1) and (-3, -5)? 02√10 02√5 10 04√5

Answer 1

Given:-

• Coordinates of Point A ( 5 , 1)
• Coordinates of Point B = (- 3, - 5)

To Find:-

• distance between the two points

Solution:-

using Formula:-

$\bigstar \: \: { \underline { \underline{ \boxed{ \sf{ Distance = \: \sqrt{(x_2 − x_1)² + (Y_2 — Y_1)²}}}}}}$

$\sf \implies \: Distance = \: \sqrt{(x_2 − x_1)² + (Y_2 — Y_1) {}^{2} }$

$\sf \implies \: Distance = \: \sqrt{(5 − ( - 3))² + (1 — ( - 5)) {}^{2} }$

$\sf \implies \: Distance = \: \sqrt{(5 + 3)² + (1 + 5) {}^{2} }$

$\sf \implies \: Distance = \: \sqrt{(8)² + (6) {}^{2} }$

$\sf \implies \: Distance = \: \sqrt{ \: 64 \: + \: \: 36 \: }$

$\sf \implies \: Distance = \: \sqrt{ \: 100 \: }$

$\bf \implies \: Distance = \: 10 \: units$

Answer 2

$\large{\underline{\underline{\pmb{\frak {\color {red}{Question:}}}}}}$

$\sf \red{what \: is \: the \: distance \: the \: points(51) \: and ( - 3 - 5)}$

$\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}$

Here,

$x_{1}$ = 5. $x_{2}$ = - 3

$y_{1}$ = 1. $y_{2 }$ = - 5

We know, Distance formula

$\red \dag \boxed{\sqrt{ (x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} } } \red \dag$

$\sqrt{( - 3 - 5 )^{2} + ( - 5 - 1)^{2} } \\ \\ \leadsto \sqrt{( - 8)^{2} + ( - 6)^{2} } \\ \\ \leadsto \sqrt{64 +36 } \\ \\ \leadsto \sqrt{100} \\ \\ \leadsto10 \: units$

Therefore, the required answer is 10 units.

I've written units because measurement is not given.

$\boxed{ \frak \red{brainlysamurai}}$