Question

Find the distance between (3,-3) and (2,7)

Answer 1

`√(101) = D`

Step-by-step Step-by-step explanation:

Method #1

We can draw a right triangle on the graph upon where the points are located and use the Pythagorean Theorem:

`{a}^(2) + {b}^(2) = {c}^(2)`

`{1}^(2) + {10}^(2) = {c}^(2)`

`1 + 100 = {c}^(2)`

`101 = {c}^(2)`

`√(101) = c`

* Whenever we talk about distance, we ONLY want the NON-NEGATIVE root.

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Method #2

Or, we can use the Distance Formula:

`\sqrt{[-x_1 + x_2]^(2) + [-y_1 + y_2]^(2)} = D`

[2, 7] [3, −3]

`\sqrt{[-3 + 2]^(2) + [3 + 7]^(2)} = D`

`\sqrt{[-1]^(2) + 10^(2)} = D`

`√(1 + 100) = D`

`√(101) = D`

** You see? It does not matter which method you choose, as long as you are doing the work correctly.

I am delighted to assist you anytime.