Question

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

Answer 1

Answer:

$\sqrt{101} = D$

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:

${a}^{2} + {b}^{2} = {c}^{2}$

${1}^{2} + {10}^{2} = {c}^{2}$

$1 + 100 = {c}^{2}$

$101 = {c}^{2}$

$\sqrt{101} = c$

* 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]

$\sqrt{[-3 + 2]^{2} + [3 + 7]^{2}} = D$

$\sqrt{[-1]^{2} + 10^{2}} = D$

$\sqrt{1 + 100} = D$

$\sqrt{101} = D$

** 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.