Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

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Presentation transcript:

Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

We will talk about 3 formulas that are used to calculate various pieces of information about pairs of points. Each formula refers to a set of two points: (x 1, y 1 ) and (x 2, y 2 )

Distance between two points A(5,3) B(18,17) 18 – 5 = 13 units 17 – 3 = 14 units AB 2 = Using Pythagoras’ Theorem, AB 2 = (18 - 5) 2 + (17 - 3) 2 y x

Distance between two points. In general, x1x1 x2x2 y1y1 y2y2 A(x 1,y 1 ) B(x 2,y 2 ) Length = x 2 – x 1 Length = y 2 – y 1 AB 2 = (y 2 -y 1 ) 2 + (x 2 -x 1 ) 2 Hence, the formula for Length of AB or Distance between A and B is y x

The Distance Formula "The Distance Formula" sung to the tune of "On Top of Old Smokey" When finding the distance Between the two points, Subtract the two x's The same for the y's. Now square these two numbers, And find out their sum. When you take the square root Then you are all done!

Ex#1: (2, 2) and (5, -2) Distance: ________

Midpoint Formula:

The Midpoint Formula "The Midpoint Formula" sung to the tune of "The Itsy Bitsy Spider" When finding the midpoint of two points on a graph, Add the two x's and cut their sum in half. Add up the y's and divide 'em by a two, Now write 'em as an ordered pair It’s the middle of the two.

Ex# 1: (2, 2) and (5, -2) Midpoint: _______

Ex M(4, 2) is the midpoint of RS. If S has a coordinates (5, -2), find the coordinates of R. R (x 1, y 1 ) S (5,-2) M(4, 2)

“Real”-world example On a road trip, you hike 3 miles north and 2miles west. Starting at the same point, your friend hikes 4 miles east and 1 mile south. How far apart are you? If you want to meet for lunch, where could you meet so each person goes the same distance?

Find the distance between a point and a line. What is the distance from point B to line q? B q (1, 4) (4, 1) (1, -2)

Example Find the distance from point A to line c.

The slope is the ratio of vertical change (rise) to horizontal change (run) of a line. Slope Formula:

Ex: (2, 2) and (5, -2) Slope: __________

(0, 3) and (-1, 1) Distance: ________ Midpoint: _______ Slope: __________