a scientist graphed the locations of the epicenter of an earthquake and all the places where the people reported feeling the earthquake. She positioned the epicenter at (1,8) and the farthest location reported to have felt the quake was positioned at (85,8). If each unit on the graph represents 1 mile, how far from its epicenter was the earthquake felt?
To find the distance from the epicenter to the farthest location where the earthquake was felt, we need to calculate the horizontal distance between the two points on the graph.
Given that each unit on the graph represents 1 mile, we can use the formula for distance between two points in a 2D plane:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, (x1, y1) represents the coordinates of the epicenter (1, 8), and (x2, y2) represents the coordinates of the farthest reported location (85, 8).
Plugging the values into the formula:
distance = √((85 - 1)^2 + (8 - 8)^2)
distance = √(84^2 + 0)
distance = √(7056)
distance ≈ 83.94 miles
Therefore, the earthquake was felt approximately 83.94 miles from its epicenter.
per the usual distance formula, that would be
√((85-1)^2 + (8-8)^2) = 84
or, you could have just noticed that both points lie on the line
y=8, and are 84 units apart