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QuestionFind the distance between marinas at P(4,2)P(4,2) and Q(8,12)Q(8,12) on a map where 1 unit = 1 km. Choices: A. 14 km B. 2292 \sqrt{29} km C. 6 km D. 252 \sqrt{5} km

Studdy Solution

STEP 1

Assumptions1. The location of marina is at coordinates (4,) . The location of marina Q is at coordinates (8,12)
3. The boat travels in a straight line from marina to marina Q4. Each unit on the map represents one kilometer

STEP 2

We can use the distance formula to calculate the 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 marinas and Q into the distance formula.
Distance=(8−)2+(12−2)2Distance = \sqrt{(8 -)^2 + (12 -2)^2}

STEP 4

Calculate the difference between the x-coordinates and the y-coordinates.
Distance=(4)2+(10)2Distance = \sqrt{(4)^2 + (10)^2}

STEP 5

Square the differences.
Distance=(16)+(100)Distance = \sqrt{(16) + (100)}

STEP 6

Add the squares.
Distance=116Distance = \sqrt{116}

STEP 7

implify the square root.
Distance=229Distance =2 \sqrt{29}So, the boat travels 2292 \sqrt{29} kilometers from marina to marina Q. The correct answer is B. 2292 \sqrt{29} kilometers.

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