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sergiy2304 [10]
4 years ago
8

20 POINTS !!! Find the distance between the points (3,-4) and (5, 4)

Mathematics
2 answers:
jeka57 [31]4 years ago
8 0

Answer:

d=2\sqrt{17}\approx8.2462

Step-by-step explanation:

To find the distance between two points, use the distance formula.

The distance formula is:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2

Let (3,-4) be x₁ and y₁ and let (5,4) be x₂ and y₂. Therefore:

d=\sqrt{(5-3)^2+(4--4)^2

Simplify:

d=\sqrt{(2)^2+(8)^2

Square:

d=\sqrt{4+64}

Add:

d=\sqrt{68}

Simplify:

d=\sqrt{4\cdot17}=\sqrt4\cdot\sqrt{17}

Simplify:

d=2\sqrt{17}\approx8.2462

Nady [450]4 years ago
5 0

Answer:

\boxed{2\sqrt{17}}

Step-by-step explanation:

To find the distance between two points, we use the distance formula. The distance formula is:

\boxed{d=\sqrt{(x_{2}-x_{1})^{2}+({y_{2}-y_{1})^{2}}}}

Therefore, we can label our coordinate pairs and solve for d.

Because we are given two coordinate pairs, we will follow the standard naming system for coordinate pairs. This is (x_{1}, y_{1}) \text \: {and} \: (x_{2}, y_{2}). Therefore, we can implement the distance formula and solve.

\sqrt{(5-3)^{2}+(4-(-4))^{2}}\\\\\sqrt{(2)^{2}+(8)^{2}}\\\\\sqrt{4 + 64} \\\\\sqrt{68} \\\\\boxed{2\sqrt{17} }

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