Distance formula 1. 1 Slope 2 2 Midpoint Formula 3.

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Presentation transcript:

Distance formula 1

1

Slope 2

2

Midpoint Formula 3

3

Point slope formula of a line 4

4

Equation of a line 5

y = mx +b m is slope b is y-intercept 5

Slope 6

6

Parallel Lines 7

Parallel lines have equal slopes 7

Perpendicular Lines 8

Perpendicular lines have opposite reciprocal slopes 8

Equation of a Circle 9

Where: Center: (h, k) and radius = 9

Finding the equation of a circle given two endpoints of the diameter 10

Use midpoint to find the center Use distance (between center and one endpoint) to find the radius Plug into equation of a circle 10

Find the equation of a perpendicular bisector 11

1.Find slope 2.Flip and change the sign of the slope from step 1. 3.Find the midpoint. 4.Plug answers from step 2 and 3 into point slope 11

Prove a parallelogram 12

Find the midpoint of both diagonals If they match then… It is a parallelogram because diagonals bisect 12

Prove a Rectangle 13

Use DISTANCE to find the length of all four sides If Both sets of opposite sides are = then… It is a rectangle because both sets of opposite sides are congruent 13

Prove a Rhombus 14

Use DISTANCE to find the length of all four sides If ALL sides are = then… It is a rhombus because all sides are congruent 14

Prove a Square 15

Use DISTANCE to find the length of all four sides and SLOPE of 2 adjacent sides If ALL sides are = and the slopes are opposite reciprocals then… It is a square because all sides are congruent and adjacent sides are perpendicular 15

Prove a Trapezoid 16

Find the SLOPE of all four sides If two slopes are = and two are then… It is a trapezoid because there is only one set of opposite parallel sides. 16

Prove an isosceles trapezoid 17

Find the SLOPE of all four sides and the DISTANCE of the non-parallel sides If two slopes are = and two are and the non-parallel sides are = then… It is an isosceles trapezoid because there is only one set of opposite parallel sides and the legs are congruent. 17