The Basics (Leaving Cert Mathematics): Flashcards

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Distance Formula
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What does the distance formula calculate?

Distance between two points in a Cartesian plane

Distance formula

d=(x2x1)2+(y2y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Distance formula is derived from which theorem?

Pythagorean theorem

What shape is used to derive the distance formula?

Right triangle

What are the legs of the triangle in distance formula?

x2x1|x_2 - x_1| and y2y1|y_2 - y_1|

Hypotenuse in distance formula derivation

Represents the distance dd

What type of line does the distance formula measure?

Straight line

Step 1: Applying distance formula

Identify coordinates (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)

Step 2: Applying distance formula

Substitute values into the formula

Step 3: Applying distance formula

Simplify to find dd

Distance from (0,0)(0,0) to (5,12)(5,12)

13 units

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