Question

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Answer 1

${\tt{\text{We\: know\:that}}}$

${\bf{\blue{Distance\:between\:two\: points=}}}$

$\sqrt{(x1 - x2) {}^{2} + (y1 - y2) {}^{2} }$

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${\bf{\text{(i)\:(4,3) \:and\:(2,5)}}}$

⇛The required distance between the points (4,3) and (2,5)

$= \sqrt{(4 - 2) {}^{2} + (3 - 5) {}^{2} } \\ = \sqrt{ {2}^{2} + ( - 2) {}^{2} } \\ = \sqrt{8} \\ \\ = \boxed{2\sqrt{2} }units$

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${\bf{\text{(ii)\:(3,4) \:and\:(5,-2)}}}$

⇛The required distance between the points (3,4) and (5,-2)

$= \sqrt{(3 - 5) {}^{2} + (4 - ( - 2)) {}^{2} } \\ = \sqrt{( - 2) {}^{2} + {6}^{2} } \\ = \sqrt{4 + 36} \\ = \boxed{ \sqrt{40} }units$

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${\bf{\text{(iii)\:(4,-6) \:and\:(-6,4)}}}$

⇛The required distance between the points (4,-6) and (-6,4)

$= \sqrt{(4 - ( - 6)) {}^{2} + ( - 6 - 4) {}^{2} } \\ = \sqrt{10 {}^{2} + ( - 10) {}^{2} } \\ = \sqrt{100 + 100} \\ = \boxed{ 10 \sqrt{2} }units$

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${\bf{\text{(iv)\:(3,4) \:and\:(7,8)}}}$

⇛The required distance between the points (3,4) and (7,8)

$= \sqrt{(3 - 7) {}^{2} + (4 - 8) {}^{2} } \\ = \sqrt{( - 4) {}^{2} + ( - 4) {}^{2} } \\ = \sqrt{16 + 16} \\ = \sqrt{32} \\ = \boxed{4 \sqrt{2} }units$