Question

Find the distance between the points A(13,2) and B(7,10)

Answer 1

Answer:

$10 = D$

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:

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

${6}^{2} + {8}^{2} = {c}^{2}$

$36 + 64 = {c}^{2}$

$100 = {c}^{2}$

$10 = c$

* 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:

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

B[7, 10] A[13, 2]

$\sqrt{[-2 + 10]^{2} + [-13 + 7]^{2}} = D$

$\sqrt{8^{2} + [-6]^{2}} = D$

$\sqrt{64 + 36} = D$

$\sqrt{100} = D$

$10 = D$

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

** 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.