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Calculate the distance between the points G=(-9, 8) and H=(-2, 2) in the coordinate plane.
Give an exact answer (not a decimal approximation).
10+
8
Distance: 0
+
-10-8
-6
-4
- 2
2
6
8
10
-S
-10

Respuesta :

rainestormee

Answer:

[tex]\sqrt{153}[/tex]

Step-by-step explanation:

Using Pythagoras in 3D.

[tex]a^2+b^2=c^2[/tex] (The distance between two points in a direction)

For the x-plane.

[tex](-9)^2+(-2)^2=c^2\\85=c^2\\c=\sqrt{85}[/tex]

For the y-plane.

[tex]8^2+2^2=c^2\\68=c^2\\c=\sqrt{68}[/tex]

Finding the shortest distance between those two points.

[tex]\sqrt{68}^2+\sqrt{85}^2=c^2\\68+85=c^2\\153=c^2\\c=\sqrt{153}[/tex]

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