Question

which of the points a(1,3), b(-3,2), c(3,4), and d (4,2) is the farthest to the origin.​

Answer 1

Answer:

c(3,4) is the farthest point from origin

Answer 2

Given,

$\[a\left( {1,3} \right),b\left( { - 3,2} \right),c\left( {3,4} \right),d\left( {4,2} \right)\]$

Solution,

Consider the distance between two points $\[\left( {{x_1},{y_1}} \right),\left( {{x_2},{y_2}} \right)\]$ ,

$\[ = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} \]$

Distance between origin O to a.

$\[O\left( {0,0} \right),a\left( {1,3} \right)\]$

$\[\begin{array}{l} = \sqrt {{{\left( {\left( {0 - 1} \right)} \right)}^2} + {{\left( {0 - 3} \right)}^2}} \\ = \sqrt {{1^2} + {3^2}} \\ = \sqrt {10} \,unit\end{array}\]$

Distance between origin O to b.

$\[\begin{array}{l}O\left( {0,0} \right),b\left( { - 3,2} \right)\\ = \sqrt {{{\left( {\left( {0 + 3} \right)} \right)}^2} + {{\left( {0 - 2} \right)}^2}} \\ = \sqrt {{3^2} + {2^2}} \\ = \sqrt {13} \,unit\end{array}\]$

Distance between origin O to c.

$\[\begin{array}{l}O\left( {0,0} \right),c\left( {3,4} \right)\\ = \sqrt {{{\left( {\left( {0 - 3} \right)} \right)}^2} + {{\left( {0 - 4} \right)}^2}} \\ = \sqrt {{3^2} + {4^2}} \\ = 5\,unit\end{array}\]$

Distance between origin O to d.

$\[\begin{array}{l}O\left( {0,0} \right),d\left( {4,2} \right)\\ = \sqrt {{{\left( {\left( {0 - 4} \right)} \right)}^2} + {{\left( {0 - 2} \right)}^2}} \\ = \sqrt {{4^2} + {2^2}} \\ = \sqrt {20} \,unit\end{array}\]$

Hence the farthest point is $\[c\left( {3,4} \right)\]$