Question

Find the distance between each of the following pair of points. ​

Answer 1

Answer:

Given:

A(2,3),B(4,1)

distance formula:

d=√((x_2-x_1)²+(y_2-y_1)²)

d=√(4-2)^2+(1-3)^2)

d=√(2)^2+(-2)^2

d=√4+4

d=√8

Answer 2

Given Points :-

• A(2,3 ) and B(4,1)

Need To Find Out :-

• The distance between A and B

Solution :-

• To find the distance between two points we have a formula called distance formula.Distance formula is as follows:-

$\pink{:\implies \sf{\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}}$

$\sf \green{Here:-}$

• $\sf{x_1 = 2\:and\:x_2 = 4}$
• $\sf{y_1 = 3\:and\:y_2 = 1}$

Now putting the values in the formula:-

$\sf\: \: \: \: \: ={\sqrt{[4 - 2]^2 + [1 - 3]^2}}$

$\sf\: \: \: \: \: ={\sqrt{[2]^2 + [-2]^2}}$

$\sf\: \: \: \: \: ={\sqrt{(4 + 4}}$

$\sf\: \: \: \: \: ={\sqrt{8}}$

$\sf\: \: \: \: \: ={\sqrt{4}\times\sqrt{2} }$

$\sf\: \: \: \: \: =\pink{{2\sqrt{2}}}$

$\therefore\:\underline{\textsf{ The distance between point A and B is \textbf{2√2cm}}}.$

Know More :-

→|| What are $\bf{x_1\:and\:x_2}$

• $\sf{x_1}$ is the abscissa (or point on x-axis) for the first coordinate. $\sf{x_2}$ is the abscissa (or the point on x-axis) for the second coordinate.

→|| What are $\bf{y_1\:and\:y_2}$

• $\sf{y_1}$ is the ordinate (or point on y-axis) for the first coordinate. $\sf{y_2}$ is the ordinate (or point in y-axis) for the second coordinate.

→|| Why is distance formula necessary?

• Distance formula is necessary as it gives the shortest distance between any two coordinates.