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Question

Question
a graph shows two points, (7,8) and (3,2)

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.

(1 point)

Answer 1

To find the distance between the two points $(7,8)$ and $(3,2)$, we can use the distance formula, which is derived from the Pythagorean Theorem. The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by:

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

In this case, we have:

• $x_1=7$, $y_1=8$
• $x_2=3$, $y_2=2$

Now we can substitute these values into the formula:

1. Calculate $x_2-x_1$ and $y_2-y_1$:

$$x_2-x_1=3-7=-4$$ $$y_2-y_1=2-8=-6$$

2. Substitute these differences into the distance formula:

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

3. Calculate the squares:

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

4. Add the squares:

$$d=\sqrt{52}$$

5. Simplify $\sqrt{52}$:

$$d=\sqrt{4\times 13}=2\sqrt{13}$$

6. Now, calculate the numerical value of $2\sqrt{13}$:

Using a calculator, $\sqrt{13}\approx 3.60555$, so:

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

7. Finally, round to the nearest hundredth:

$$d\approx 7.21$$

Thus, the length between the two points is approximately 7.21.