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(D) Let the starting point $A$ be at the origin $(0, 0)$ in a Cartesian coordinate system.Moving $800 \, m$ north takes the person to point $B(0, 800)

Vedclass · Accepted Answer

$1300$

Vedclass · Answer

(D) Let the starting point $A$ be at the origin $(0, 0)$ in a Cartesian coordinate system.Moving $800 \, m$ north takes the person to point $B(0, 800)$.Moving $500 \, m$ east from $B$ takes the person to point $C(500, 800)$.Moving $400 \, m$ north from $C$ takes the person to point $D(500, 800 + 400) = D(500, 1200)$.The direct distance from $A(0, 0)$ to $D(500, 1200)$ is given by the distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.$d = \sqrt{(500 - 0)^2 + (1200 - 0)^2} = \sqrt{500^2 + 1200^2}$.$d = \sqrt{250000 + 1440000} = \sqrt{1690000}$.$d = 1300 \, m$.

$A$ person begins his journey from point $A$. From $A$,he moves $800 \, m$ towards north to reach point $B$. From $B$,he moves $500 \, m$ towards east to reach point $C$. From $C$,he moves $400 \, m$ towards north to reach point $D$. Find the direct distance in $m$ from $A$ to $D$.

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