1. The problem asks us to determine if John and Miles beat or missed their goal of canoeing at least 14 miles based on the graph. 2. The path starts at point $(-7,-2)$ and ends at point $(7,2)$ on the coordinate plane. 3. To find the distance they traveled, we use the distance formula between two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$: $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$ 4. Substitute the coordinates: $$d=\sqrt{(7-(-7))^2+(2-(-2))^2}=\sqrt{(7+7)^2+(2+2)^2}=\sqrt{14^2+4^2}$$ 5. Calculate the squares: $$d=\sqrt{196+16}=\sqrt{212}$$ 6. Simplify the square root: $$d=\sqrt{4\times53}=2\sqrt{53}$$ 7. Approximate $\sqrt{53}$: $$\sqrt{53}\approx7.28$$ 8. So, $$d\approx2\times7.28=14.56$$ 9. Their goal was 14 miles, and they traveled approximately 14.56 miles. 10. Calculate how much they beat their goal by: $$14.56-14=0.56$$ 11. The closest option to beating the goal by about 0.3 miles is option C, but 0.56 is closer to 0.5 than 0.3. 12. Since none of the options exactly match 0.56, the best fit is that they beat their goal by about 0.3 miles (option C). Final answer: They beat their goal by about 0.3 miles (option C).