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QuestionCalculate the distance between points A(4,9) and B(2,-3) using the formula d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

Studdy Solution

STEP 1

Assumptions1. The coordinates of point A are (4,9) . The coordinates of point B are (,-3)
3. We are using the Euclidean distance formula to calculate the distance between two points in a plane.

STEP 2

The distance between two points (x1, y1) and (x2, y2) in a plane can be calculated using the Euclidean distance formulaDistance=(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 points A and B into the formula.
Distance=(2−)2+(−3−9)2Distance = \sqrt{(2 -)^2 + (-3 -9)^2}

STEP 4

Calculate the differences (2 -4) and (-3 -9).
Distance=(−2)2+(−12)2Distance = \sqrt{(-2)^2 + (-12)^2}

STEP 5

Square the differences -2 and -12.
Distance=4+144Distance = \sqrt{4 +144}

STEP 6

Add the squared differences.
Distance=148Distance = \sqrt{148}

STEP 7

Calculate the square root of148.
Distance=148≈12.17Distance = \sqrt{148} \approx12.17The distance between the points A(4,9) and B(2,-3) is approximately12.17 units.

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