Question

Find the distance between points M and N. and if anyone could kinda explain how they got it so i can do the next ones on my own

Answer 1

See photo for steps and the answer is square root of 13

Answer 2

Answer:

$\sqrt{13} = D$

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:

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

${3}^{2} + {2}^{2} = {c}^{2}$

$9 + 4 = {c}^{2}$

$13 = {c}^{2}$

$\sqrt{13} = c$

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

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Method #2

We can use the Distance Formula:

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

N[−3, 2] M[−6, 0]

$\sqrt{[3 - 6]^{2} + [0 + 2]^{2}} = D$

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

$\sqrt{9 + 4} = D$

$\sqrt{13} = D$

* 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.