Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth. (1 point). the cordinates are (3,2) going to (7,8)

Answer 1

To find the length between the two points $(3,2)$ and $(7,8)$, we can apply the Pythagorean theorem. First, we need to find the distance between the two points using the distance formula, which is derived from the Pythagorean theorem.

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated using the formula:

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

In our case, the points are:

• $(x_1,y_1)=(3,2)$
• $(x_2,y_2)=(7,8)$

Now, we can compute the differences in the coordinates:

$$x_2-x_1=7-3=4$$

$$y_2-y_1=8-2=6$$

Now, we can plug these values into the distance formula:

$$d=\sqrt{(4{)}^2+(6{)}^2}$$

Calculating the squares:

$$d=\sqrt{16+36}$$

$$d=\sqrt{52}$$

Now we can simplify $\sqrt{52}$:

$$\sqrt{52}=\sqrt{4\cdot 13}=2\sqrt{13}$$

Now approximating $\sqrt{13}\approx 3.60555$:

$$d\approx 2\times 3.60555\approx 7.2111$$

Rounding to the nearest hundredth:

$$d\approx 7.21$$

Thus, the length between the two points $(3,2)$ and $(7,8)$ is approximately 7.21.