Question

Jefferson is making a map of New York on a coordinate grid. He plots Binghamton at point B(1, -3) and Schenectady at point S(7, 1). These cities are connected by I-88. If each unit on Jefferson’s map represents 18 miles, what is the distance from Binghamton and Schenectady along I-88? Round to the nearest mile.

A.104miles
B.118miles
C.125miles
D.130miles"

Answer 1

The distance between the points B(1, -3) and S(7, 1) on a coordinate grid is 2√13 map units. Converting to miles using the scale where 1 unit equals 18 miles, the actual distance is about 130 miles after rounding to the nearest mile.

Step-by-step explanation:

The question involves calculating the distance between two points on a coordinate grid where each unit represents a certain distance in miles. To find the distance between Binghamton at point B(1, -3) and Schenectady at point S(7, 1) along I-88, we can use the distance formula:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

Plugging in our coordinates, we get:

d = √[(7 - 1)^2 + (1 - (-3))^2]

d = √[(6)^2 + (4)^2]

d = √[36 + 16]

d = √52

d = √(4·13)

d = 2√13

Now we can convert the units from map units to actual miles, bearing in mind that each unit represents 18 miles:

Actual distance = d × 18 miles/unit

Actual distance = 2√13 × 18

Actual distance = 36√13

Actual distance ≈ 36 * 3.605 (approximate value of √13)

Actual distance ≈ 129.78 miles

When rounded to the nearest mile, the distance from Binghamton to Schenectady is approximately 130 miles. So, the correct answer is D. 130 miles.