2. Find the distances of the following points from the origin.
2. Find the distances of the following points from the origin.

Distance – The length along a line or line segment between two points on the line or line segment.

Section formula define – The section formula helps in finding the coordinates of a point dividing the coordinates of a point dividing a given line segment into two parts such that their lengths are in a given ratio.

(c) \left( 8,15 \right)

Solution:-

OriginA=\left( 0,0 \right),B=\left( 8,15 \right)

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

Where,{{x}_{1}}=ycoordinate ofA=0

{{y}_{1}}=ycoordinate ofA=0

{{x}_{2}}=xcoordinate ofB=8

{{y}_{2}}=ycoordinates ofB=15

=\sqrt{\left( {{\left( 8-0 \right)}^{2}}+{{\left( 15-0 \right)}^{2}} \right)}

=\sqrt{\left( {{\left( 8 \right)}^{2}}+{{\left( 15 \right)}^{2}} \right)}

=\sqrt{\left( 64+225 \right)}

=\sqrt{289}units

=17units

(d) \left( 0,11 \right)

Solution:-

OriginA=\left( 0,0 \right),B=\left( 0,11 \right)

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

Where,x{}_{1}=xcoordinate ofA=0

{{y}_{1}}=ycoordinate ofA=0

{{x}_{2}}=xcoordinate ofB=0

{{y}_{2}}=ycoordinates ofB=11

=\sqrt{\left( {{\left( 0-0 \right)}^{2}}+{{\left( 11-0 \right)}^{2}}\right)}

=\sqrt{\left( {{\left( 0 \right)}^{2}}+{{\left( 11 \right)}^{2}} \right)}

=\sqrt{\left( 0+121 \right)}

=\sqrt{121}units

=11units