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QuestionFind the distance from the Tax Office at (−1.5,−1)(-1.5,-1) to the Gas Station at (3,4)(3,4), rounded to the nearest tenth.

Studdy Solution

STEP 1

Assumptions1. The Tax Office is located at the midpoint (-1.5, -1) . The Gas Station is located at (3,4)
3. Each unit represents one mile4. We are looking for the shortest distance, which is a straight line

STEP 2

We will use the distance formula to find the shortest distance between two points in a plane. The distance formula is derived from the Pythagorean theorem and is given byDistance=(x2−x1)2+(y2−y1)2Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}

STEP 3

Now, plug in the given values for the coordinates of the Tax Office (x1, y1) and the Gas Station (x2, y2) into the distance formula.
Distance=(3−(−1.5))2+(−(−1))2Distance = \sqrt{(3 - (-1.5))^2 + ( - (-1))^2}

STEP 4

implify the expression inside the square root.
Distance=(3+1.)2+(4+1)2Distance = \sqrt{(3 +1.)^2 + (4 +1)^2}

STEP 5

Perform the addition inside the parentheses.
Distance=(4.5)2+(5)2Distance = \sqrt{(4.5)^2 + (5)^2}

STEP 6

Square the numbers inside the square root.
Distance=(20.25)+(25)Distance = \sqrt{(20.25) + (25)}

STEP 7

Perform the addition inside the square root.
Distance=45.25Distance = \sqrt{45.25}

STEP 8

Take the square root of45.25.
Distance=6.7Distance =6.7So, the shortest distance from the new Tax Office to the Gas Station is6.7 miles.

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