[tex]RS = \sqrt{(b-0)^{2}+(c-a)^{2}}[/tex] and RS is simplified to [tex]RS = \sqrt{a^{2}+b^{2}+c^{2}-2ac}[/tex]
Step-by-step explanation:
We know that , Distance between any two points [tex](x_1 , y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by formula :
[tex]Distance = \sqrt{(x_1-x_2)^{2}+(y_1-y_2)^{2}}[/tex]
In this question , we have [tex]R(0,a)[/tex] and [tex]S(b,c)[/tex] .
We need to simplify RS which is given by:
[tex]Distance = \sqrt{(x_1-x_2)^{2}+(y_1-y_2)^{2}}[/tex]
⇒ [tex]Distance = \sqrt{(x_1-x_2)^{2}+(y_1-y_2)^{2}}[/tex]
⇒ [tex]RS = \sqrt{(x_1-x_2)^{2}+(y_1-y_2)^{2}}[/tex]
⇒ [tex]RS = \sqrt{(0-b)^{2}+(a-c)^{2}}[/tex]
⇒ [tex]RS = \sqrt{(b-0)^{2}+(c-a)^{2}}[/tex]
We know that , [tex](a-b)^{2} = a^{2}+b^{2}-2ab[/tex]
⇒ [tex]RS = \sqrt{b^{2}+c^{2}+a^{2}-2ac}[/tex]
⇒ [tex]RS = \sqrt{a^{2}+b^{2}+c^{2}-2ac}[/tex]
∴ [tex]RS = \sqrt{(b-0)^{2}+(c-a)^{2}}[/tex] and RS is simplified to [tex]RS = \sqrt{a^{2}+b^{2}+c^{2}-2ac}[/tex].
