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QuestionFind the distances between points A(4,9), B(-2,-3), and C(0,0). Round to the nearest tenth.

Studdy Solution

STEP 1

Assumptions1. The coordinates of point A are (4,9) . The coordinates of point B are (-,-3)
3. The coordinates of point C are (0,0)
4. We are using the Euclidean distance formula to calculate the distance between two points in a plane.

STEP 2

The Euclidean distance between two points (x1, y1) and (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

First, let's calculate the distance between points A and B. Substitute the coordinates of points A and B into the distance formula.
DistanceAB=((−2)−)2+((−3)−9)2Distance_{AB} = \sqrt{((-2) -)^2 + ((-3) -9)^2}

STEP 4

Calculate the distance between points A and B.
DistanceAB=((−6)2+(−12)2)=36+144=180≈13.4Distance_{AB} = \sqrt{((-6)^2 + (-12)^2)} = \sqrt{36 +144} = \sqrt{180} \approx13.4

STEP 5

Next, calculate the distance between points A and C. Substitute the coordinates of points A and C into the distance formula.
DistanceAC=(0−4)2+(0−9)2Distance_{AC} = \sqrt{(0 -4)^2 + (0 -9)^2}

STEP 6

Calculate the distance between points A and C.
DistanceAC=(−4)2+(−9)2=16+81=97≈9.8Distance_{AC} = \sqrt{(-4)^2 + (-9)^2} = \sqrt{16 +81} = \sqrt{97} \approx9.8

STEP 7

Finally, calculate the distance between points B and C. Substitute the coordinates of points B and C into the distance formula.
DistanceBC=(0−(−2))2+(0−(−3))2Distance_{BC} = \sqrt{(0 - (-2))^2 + (0 - (-3))^2}

STEP 8

Calculate the distance between points B and C.
DistanceBC=(2)2+(3)2=4+=13≈3.6Distance_{BC} = \sqrt{(2)^2 + (3)^2} = \sqrt{4 +} = \sqrt{13} \approx3.6So, the distance between points A and B is approximately13.4 units, the distance between points A and C is approximately.8 units, and the distance between points B and C is approximately3.6 units.

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