Find the distance between the following pairs of points:
Find the distance between the following pairs of points:

(i) (2, 3), (4, 1)

(ii) (-5, 7), (-1, 3)(iii) (a, b), (- a, – b)

We know that formula to find the distance (d) between two points \left( {{x}_{1}},{{y}_{1}} \right)and \left( {{x}_{2}},{{y}_{2}} \right) is:

d=\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}

(i) Given, the pair of points is (2, 3), (4, 1).

The distance between these two points is:

    <span class="ql-right-eqno"> (1) </span><span class="ql-left-eqno">   </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4ec9a1a959ed994e1b82f0b587785b12_l3.png" height="231" width="1761" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} <!-- /wp:paragraph --> <!-- wp:paragraph -->  & d=\sqrt{{{\left( 4-2 \right)}^{2}}+{{\left( 1-3 \right)}^{2}}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph -->  & =\sqrt{{{2}^{2}}+{{\left( -2 \right)}^{2}}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph -->  & =\sqrt{8} \\ <!-- /wp:paragraph --> <!-- wp:paragraph -->  & =2\sqrt{2}  <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{align*}" title="Rendered by QuickLaTeX.com"/>

(ii) Given, the pair of points is (-5, 7), (-1, 3).

The distance between these two points is:

    <span class="ql-right-eqno"> (2) </span><span class="ql-left-eqno">   </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ba1e46135b1aa50835226db4e4ac5195_l3.png" height="231" width="1761" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} <!-- /wp:paragraph --> <!-- wp:paragraph -->  & d=\sqrt{{{\left( -1+5 \right)}^{2}}+{{\left( 3-7 \right)}^{2}}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph -->  & =\sqrt{{{4}^{2}}+{{\left( -4 \right)}^{2}}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph -->  & =\sqrt{32} \\ <!-- /wp:paragraph --> <!-- wp:paragraph -->  & =4\sqrt{2}  <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{align*}" title="Rendered by QuickLaTeX.com"/>

(iii) Given, the pair of points is (a, b), (- a, – b).

The distance between these two points is:

    <span class="ql-right-eqno"> (3) </span><span class="ql-left-eqno">   </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-96557a14f63463dbcff1cf9d22be8d08_l3.png" height="181" width="1220" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} <!-- /wp:paragraph --> <!-- wp:paragraph -->  & d=\sqrt{{{\left( -a-a \right)}^{2}}+{{\left( -b-b \right)}^{2}}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph -->  & =\sqrt{{{\left( -2a \right)}^{2}}+{{\left( -2b \right)}^{2}}} \\ <!-- /wp:paragraph --> <!-- wp:paragraph -->  & =2\sqrt{{{a}^{2}}+{{b}^{2}}}  \end{align*}" title="Rendered by QuickLaTeX.com"/>