Question

The robot is moving from its origin (base) as per the following log:


Find the final coordinates (x,y) of the robot.

• A. (2/5,1/3)
• B. (3/7,3/5)
• C. (2/5,14/15)
• D. (2/5,14/15)

Answer 1

The correct option is D (2/5,14/15)

First, let's use commutative and associative properties respectively to group the numbers with the same denominator together.

So,
Final x-coordinate
= $\frac{3}{7}$ + $\frac{2}{5}$ + (-$\frac{3}{7}$)
= {$\frac{3}{7}$ + (-$\frac{3}{7}$)} + $\frac{2}{5}$ [by associative property]
= 0 + $\frac{2}{5}$ [by additive inverse]
= $\frac{2}{5}$ [by additive identity]

Similarly,
Final y-coordinate
= $\frac{3}{5}$ + $\frac{1}{3}$ + 0
= {$\frac{3}{5}$ + ($\frac{1}{3}$ )} + 0
= $\frac{9+5}{15}$
= $\frac{14}{15}$

Hence, the final coordinates of the robot are (2/5,14/15).