Two students are using the distance formula to determine the distance between (9, 4) and (–3, 8) on a coordinate grid. Their work is shown below.

The differences are 12 for one student and -12 for the other student, and -4 for one student and 4 for the other student. The differences are clearly different as they are additive inverses of each other, but since the differences are squared, the numbers become the same after squaring.

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HafsaM HafsaM · Answer 2 · 2022-05-31T13:27:52+02:00

Plus and minus signs are positive when squared.

Option (A) is correct

There difference are each squared.

What is square of positive and negative numbers?

"The square of a number can be found by multiplying the number by itself. The product of two negative numbers is always positive."

Given

The distance between (9, 4) and (–3, 8) on a coordinate grid

By comparing Karlin's and Abby's work, we get

9 - (-3) = - [-3 - 9]

Squaring on both sides

[tex][9 - (-3)]^{2} = [- [-3 - 9]]^{2}[/tex]

[tex][9 +3]^{2} = [- [-12]]^{2}[/tex]

[tex][12]^{2} = [12]^{2}[/tex]

4 - 8 = - [8 - 4]

Squaring on both sides

[tex][4 - 8 ]^{2} =[ - [8 - 4]]^{2}[/tex]

[tex][-4 ]^{2} =[ - 4]^{2}[/tex]

Plus and minus signs are positive when squared.

Hence, There difference are each squared.

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