Math

QuestionCalculate the distance between the points (2,5)(2,5) and (2,1)(-2,-1).

Studdy Solution

STEP 1

Assumptions1. The coordinates of the first point are (,5) . The coordinates of the second point are (-,-1)
3. We are working in a-dimensional Cartesian coordinate system

STEP 2

The distance between two points (x1,y1)(x1, y1) and (x2,y2)(x2, y2) in a2-dimensional Cartesian coordinate system is given by the formulaDistance=(x2x1)2+(y2y1)2Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}

STEP 3

Now, plug in the given values for (x1,y1)(x1, y1) and (x2,y2)(x2, y2) into the formula.
Distance=(22)2+(15)2Distance = \sqrt{(-2 -2)^2 + (-1 -5)^2}

STEP 4

Calculate the squares inside the square root.
Distance=(4)2+(6)2Distance = \sqrt{(-4)^2 + (-6)^2}

STEP 5

Calculate the squares.
Distance=16+36Distance = \sqrt{16 +36}

STEP 6

Add the numbers inside the square root.
Distance=52Distance = \sqrt{52}

STEP 7

implify the square root, if possible. In this case, 52\sqrt{52} does not simplify nicely, so we can leave it as is or approximate it as a decimal.
The distance between the points (2,5)(2,5) and (2,1)(-2,-1) is 52\sqrt{52} or approximately7.21 units.

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