The Straight Line10 cards

Tagged as: geometry

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1

Distance Formula

D=v(x2-x1)² +(y2-y1)²

2

Midpoint

(x1+x2/2 , y1+y2/2)

3

Gradient

m= y2-y1/x2-x1 m= Vertical distance Horizontal Distance m= tan? Tan ? = opp/ adj

4

Special Gradients

A line goin up diagonally from left to right is a POSITIVE gradient A line going down diagonally from left to right is a NEGATIVE gradient A line parallel to the x-axis has no graduent ( y= a number) A line parallel to the y-axis is an undefined

5

Vocab

PARRALLEL- two lines with equal gradients COLLINEAR- Two lines with a point in common PERPENDICULAR- Two lines which meet at right angles MEDIAN- Straight line from a vertex meets the opposite side in the middle ALTITUDE-straight line from a vert

6

Equations

Y=mx+c Ax+By+C=0 y-b=m(x-a)

7

Calculating Perpendicular Bisectors

Step 1- Draw Diagram Step 2- find the gradient of the line Step 3- Find the perpendicular gradient Step 4- Find midpoint Step 5- Substitute into Equation y-b=m(x-a)

8

Finding the equation of median

-Draw Sketch -Find midpoint of opposite -Find gradient of median -sub into Equation (y-b=m(x-a)) -Tidy Up

9

Finding equation of an altitude

-Draw Sketch -Find gradient of opposite side -Find Perpendicular Gradient -sub into equation (y-b=m(x-a)) -Tidy up

10

More Vocab

CIRCUMCENTRE- Point of intersection of perpendicular bisectors ORTHOCENTRE- Point of interection of altitudes CENTEOID- Oint of intersection of medians