Distance/Midpoint Formula (Junior Cert Mathematics): Flashcards

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Distance/Midpoint Formula
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Distance formula for points A(x1,y1)A(x_1,y_1) and B(x2,y2)B(x_2,y_2)

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

Purpose of distance formula

Find how far apart two points are on the Cartesian Plane

Midpoint formula

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

What is a midpoint?

Point exactly halfway between two points on a line segment

First step when using distance/midpoint formulas

Label the points as x1x_1, y1y_1, x2x_2, y2y_2

Why use brackets when substituting values?

To avoid mistakes, especially with negative numbers

Order of operations for distance formula

Brackets, exponents, then addition

Distance between A(2,3)A(2,3) and B(5,7)B(5,7)

55 units

Midpoint of segment from A(2,3)A(2,3) to B(8,7)B(8,7)

(5,5)(5, 5)

How to find x-coordinate of midpoint

Add both x-coordinates and divide by 22

How to find y-coordinate of midpoint

Add both y-coordinates and divide by 22

What does AB|AB| represent?

Distance between points AA and BB

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