Apply the Pythagorean Theorem to find the length between (−1, 6)

Question

and (5, −2)
. Round your answer to the nearest hundredth, if necessary.

Answer 1

To find the distance between the points $(-1,6)$ and $(5,-2)$, 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 the formula:

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

Let's assign the coordinates:

• $x_1=-1$
• $y_1=6$
• $x_2=5$
• $y_2=-2$

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

$$d=\sqrt{(5-(-1){)}^2+(-2-6{)}^2}$$

Calculating $5-(-1)$:

$$5+1=6$$

Calculating $-2-6$:

$$-2-6=-8$$

Now substituting these values back into the formula, we have:

$$d=\sqrt{(6{)}^2+(-8{)}^2}$$

Calculating $6^2$ and $(-8{)}^2$:

$$6^2=36$$ $$(-8{)}^2=64$$

Now summing these:

$$d=\sqrt{36+64}=\sqrt{100}$$

Finally, taking the square root gives us:

$$d=10$$

Thus, the distance between the points $(-1,6)$ and $(5,-2)$ is $10$. Rounding is not necessary here as it is a whole number.

Final Answer: 10