Distance and Midpoints (VCE SSCE Mathematical Methods): Flashcards

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Distance and Midpoints
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What is a midpoint of a line segment?

Point exactly halfway between two endpoints

How to find midpoint coordinates

Average the xx-coordinates and average the yy-coordinates

Midpoint formula for (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)

(x1+x22,y1+y22)\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)

Vertical line: which coordinate stays constant?

The xx-coordinate remains constant

Horizontal line: which coordinate stays constant?

The yy-coordinate remains constant

Distance formula for (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)

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

Which theorem derives the distance formula?

Pythagoras' theorem

Midpoint gives what type of output?

A point (ordered pair)

Distance gives what type of output?

A number (length)

Horizontal distance between two points

x2x1x_2 - x_1

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