Question

A cartographer has plotted the locations of a lighthouse and all the islands in the vicinity. The lighthouse is positioned at (-8, 7), and the farthest island is located at (61, 7). If each unit on the graph represents 1 mile, what is the distance from the lighthouse to the farthest island in miles?

A) 69 miles
B) 54 miles
C) 68 miles
D) 62 miles
E) 59 miles

Answer 1

The distance from the lighthouse to the farthest island is 69 miles.

Step-by-step explanation:

To find the distance from the lighthouse to the farthest island, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and calculates the distance between two points in a coordinate plane. The formula is:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values from the given coordinates, we get:

Distance = sqrt((61 - (-8))^2 + (7 - 7)^2)

Calculating this, we get:

Distance = sqrt(69^2 + 0^2) = 69 miles