Question

ex 7.1 class 10

find the distance formula:

(-5, 7) , (-1, 3)​

Answer 1

Given : Here, two points are given. Let the name of the points be P (-5, 7) and Q(-1, 3).

To Find : Distance between these points.

⠀⠀⠀ ⠀⠀____________________

• We know that formula for finding distance between two points is

$\large{\boxed{\sf{distance = \sqrt{(x_{2} -x_{1}) {}^{2} - (y_{2} - y_{2}) {}^{2} } }}}$

$\:$

$\tt : \implies \: d \: = \sqrt{( - 1 + 5) {}^{2} - (3 - 7) {}^{2} }$

$\:$

$\tt : \implies \: d = \sqrt{( 4) {}^{2} - ( - 4) {}^{2} }$

$\:$

$\tt : \implies \: d = \sqrt{16 + 16}$

$\:$

$\tt : \implies \: d = \sqrt{32}$

$\:$

$\tt : \implies \: d = 4 \sqrt{2} \: units$

$\:$

$\sf\therefore{\underline{Hence, \: the \: distance \: between \: the \: points \: is \: \bold{4 \sqrt{2}} \: units. }}$