Question

The book wants me to use the Pythagorean Theorem (a^2+b^2=c^2) to get the correct answer. I never learned how to use the theorem when finding distance and have only used Distance Formula. I tried using the Distance Formula to get the correct answer and got a negative outcome. Can someone please explain how Pythagorean Theorem works or maybe tell me how to fix the Distance Formula so it doesn't give me a negative outcome.​

Answer 1

Answer:

C) $\sqrt{106}$ units

Step-by-step explanation:

The Pythagorean Theorem is $a^2+b^2=c^2$ where $a$ and $b$ are side lengths of a right triangle and $c$ is the hypotenuse, the longest side of the right triangle.

The distance formula is similar to that of the Pythagorean Theorem which is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ where $(x_1,y_1)$ and $(x_2,y_2)$ are the points that you wish to find the distance between them in an (x,y) coordinate plane.

Here, we are given that $(x_1,y_1)$ is $P(-4,-6)$ and $(x_2,y_2)$ is $Q(1,3)$. So, we can use the distance formula as described previously to find the positive distance between the two points:

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

$d=\sqrt{(1-(-4))^2+(3-(-6))^2}$

$d=\sqrt{(1+4)^2+(3+6)^2}$

$d=\sqrt{(5)^2+(9)^2}$

$d=\sqrt{25+81}$

$d=\sqrt{106}$

$d \approx 10.295630141$

Since all of the given answer choices are in radical form, then C is the correct answer. The distance between the two points is $\sqrt{106}$ units.