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

C)
`√(106)` units

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=√((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=√((x_2-x_1)^2+(y_2-y_1)^2)`

`d=√((1-(-4))^2+(3-(-6))^2)`

`d=√((1+4)^2+(3+6)^2)`

`d=√((5)^2+(9)^2)`

`d=√(25+81)`

`d=√(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
`√(106)` units.