SOLUTION: Your travel guide contains a grid map of Rome, with each unit on the grid representing 0.5 kilometers. If the Sistine Chapel is located at (−1,−4) and Trevi Fountain is loc

Question 1205270: Your travel guide contains a grid map of Rome, with each unit on the grid representing 0.5
kilometers. If the Sistine Chapel is located at (−1,−4)
and Trevi Fountain is located at (3,−5)
, what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two landmarks in kilometers?
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

the distance between (,) and (,) on the map is

with each unit on the grid representing , the direct distance will be

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Plot the points (-1,-4) and (3,-5) on the same xy grid.
Draw a segment to connect them. This forms the hypotenuse of a right triangle.

The horizontal leg of this right triangle is the distance between x coordinates.
The distance from x = -1 to x = 3 is 4 units.

The vertical leg of this right triangle is the distance between y coordinates.
The distance from x = -4 to x = -5 is 1 unit.

This right triangle has legs of a = 1 and b = 4
The hypotenuse c is the distance between (-1,-4) and (3,-5)
Apply the Pythagorean Theorem to find c.
a^2 + b^2 = c^2
c = sqrt( a^2+b^2 )
c = sqrt( 1^2 + 4^2 )
c = sqrt(17)
c = 4.1231 units approximately

Because each unit represents 0.5 km, it means 4.1231 units = 4.1231*0.5 = 2.06155

Answer: The distance between the two landmarks is roughly 2.06 km

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