Question

the grid shows the locations of 3 bus stops.
neil’s home is located at (0, −4). neil is limited to walk only horizontally and vertically. each unit on the grid represents (\frac{1}{4}) mile.
what is the minimum distance, in miles, neil would need to walk to reach a bus stop from his home? enter the answer in the box.
miles

Explanation:

Step1: Calculate Manhattan distance for each stop

Manhattan distance formula: $d = |x_2 - x_1| + |y_2 - y_1|$

1. For $(-2, 3)$: $| -2 - 0 | + |3 - (-4)| = 2 + 7 = 9$ units
2. For $(-8, -7)$: $| -8 - 0 | + |-7 - (-4)| = 8 + 3 = 11$ units
3. For $(7, -1)$: $|7 - 0| + |-1 - (-4)| = 7 + 3 = 10$ units

Step2: Find minimum grid distance

Minimum grid distance = 9 units

Step3: Convert to miles (1 unit = $\frac{1}{4}$ mile)

$9 \times \frac{1}{4} = \frac{9}{4} = 2.25$

Answer:

2.25