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QuestionCalculate the distance between points A(4,9) and C(9,0) 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 C are (9,0)
3. We are using the Euclidean distance formula to find the distance between two points in a plane.

STEP 2

The Euclidean distance between two points A(x1, y1) and C(x2, y2) in a plane is given by the 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 C into the distance formula.
Distance=(9−)2+(0−9)2Distance = \sqrt{(9 -)^2 + (0 -9)^2}

STEP 4

Calculate the difference between the x-coordinates and the y-coordinates.
Distance=()2+(−9)2Distance = \sqrt{()^2 + (-9)^2}

STEP 5

Square the differences.
Distance=(25)+(81)Distance = \sqrt{(25) + (81)}

STEP 6

Add the squared differences.
Distance=106Distance = \sqrt{106}The distance between points A(4,9) and C(9,0) is √106 units.

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