Question

question 2 the town of lakehorn is built on a grid system. town hall is located downtown at point (0,0). a new school is located 3 miles north and 2 miles east of town hall. only students who live outside a 5 - mile radius from the school are eligible to ride the school bus. which of the following students are eligible to ride the bus? select all that apply. charity lives 1 mile due south of town hall. thomas lives 3 miles south and 4 miles east of the school. kaleb lives 2 miles south and 4 miles east of the town hall. marinna lives 2 miles north and 3 miles west of the town hall. 4 pts

Explanation:

Step1: Find the school's coordinates

The school is located 3 miles north and 2 miles east of town - hall (at the origin \((0,0)\)). So the school's coordinates are \((2,3)\).

Step2: Use the distance - formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) to find the distance of each student from the school

For Charity:
Charity lives 1 mile due south of town - hall, so her coordinates are \((0, - 1)\).
\[d_{Charity}=\sqrt{(2 - 0)^2+(3-( - 1))^2}=\sqrt{4 + 16}=\sqrt{20}\approx4.47<5\]
For Thomas:
Thomas lives 3 miles south and 4 miles east of the school. His coordinates are \((2 + 4,3 - 3)=(6,0)\).
\[d_{Thomas}=\sqrt{(6 - 2)^2+(0 - 3)^2}=\sqrt{16 + 9}=\sqrt{25}=5\]
For Kaleb:
Kaleb lives 2 miles south and 4 miles east of town - hall, so his coordinates are \((4,-2)\).
\[d_{Kaleb}=\sqrt{(2 - 4)^2+(3-( - 2))^2}=\sqrt{4 + 25}=\sqrt{29}\approx5.39>5\]
For Marinna:
Marinna lives 2 miles north and 3 miles west of town - hall, so her coordinates are \((-3,2)\).
\[d_{Marinna}=\sqrt{(2-( - 3))^2+(3 - 2)^2}=\sqrt{25 + 1}=\sqrt{26}\approx5.1>5\]

Answer:

Thomas, Charity