Answer
The point $A$ is closer to the origin
Work Step by Step
$A(6,7);$ $B(-5,8)$
The distance between two points is given by the formula $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$
Find the distance between point $A$ and the origin. For these two points, $x_{1}=6$, $y_{1}=7$, $x_{2}=0$ and $y_{2}=0$.
Substitute the known values into the formula:
$d_{AO}=\sqrt{(0-6)^{2}+(0-7)^{2}}=\sqrt{(-6)^{2}+(-7)^{2}}=...$
$...=\sqrt{36+49}=\sqrt{85}\approx9.2195$
Find the distance between point B and the origin. For these two points, $x_{1}=-5$, $y_{1}=8$, $x_{2}=0$ and $y_{2}=0$.
Substitute the known values into the formula:
$d_{BO}=\sqrt{(0+5)^{2}+(0-8)^{2}}=\sqrt{5^{2}+(-8)^{2}}=...$
$...=\sqrt{25+64}=\sqrt{89}\approx9.434$
Since $d_{AO}\lt d_{BO}$, the point $A$ is closer to the origin
