Question

20 POINTS !!!

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

Answer 1

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:

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

Answer 2

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.

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