Math

• A formula that us used to find the distance of the two points on the place

  Distance formula
• Find A distance

  1. (2,-1), (3,4)

  D=√26

  2. (3,6), (4,-2)

  D=√65

  3. (4,7) (6,-4)

  D=5,√5

  4. (2,-1) (3,4)

  D=√26

  5. (3,4) , (6,8)

  D=5

  6. (10,7),(4,15)

  D=10
• Midpoint -It is the middle point of the given two point

  (x¹+x²/2,y¹+y²/2)
• Midpoint

  (-2,3) (3,-9)

  M(x,y)=3

  (3,5), (4,-6)

  M(x,y)=-7/4
• Using the distance formula in proving geometry properties
• Triangle PqR with coordinates P(-3,-2) Q(-1,3) R(1,-2) show that ∆ PQR is isosceles triangle

  PQ-RQ

  D=√29
• Finding the distance between a point and a line

  -the short distance between a point and a line is the segment from the point going perpendicular to the line.
• 1.Distance between points and linthe Shortest distance from (-1,2) to 3x-4y+1=0 D=2

  2.find this shortest distance between the point (10,14) and the line 8x-6y+16=0

  D= 6/5 or 1.2

  3.(-4,6) 3x+4y=-10

  D= 4.4

  4. (1,7) Y=2x-8

  D=2.6
• Slope of a line given two points

  (3,4) And (5,-2)

  =-3

  (-4,-5) And (7,-2)

  =3/11

  (3,-4) And (8,9)

  = 13/5
• 1.write the explanation of the circle in center radius form whose center is at (3,-2) and has a radius of 11

  (X-3)²+(y+2)²=121

  2.writw the standard form of the equation of the circle with center at the origin and radius 7

  X²+y²=49

  3.(-4,-1) And radius=5

  Center=(-4,-1)

  Radius=5

  (X+4)²+(y-1)²=5²

  (X+4)²+(y-1)²=25

  4. Point of origin

  X²+y²=6

  X²+y²=36
• Find the center and radius of the following equation

  1.x²+y²=49

  Radius=7

  Center=(0,0)

  2.(X-8)²+(y+7)²=121

  Radius =(8,-7)

  Center=11

  3.find the center the radius of the circle of the equation (x-4)+(y-3)=36

  Center=(4,3)

  Radius=6

  4.write the equation of the circle if the center is (7,-5) and radius of 8cm

  (X+h)²+(y-k)²=8²

  (X-7)²+(y+5)²=64cm

  5.9x²+9y²=4

  Center=(0,0)

  Radius=2/3

  6.(,x-5)²+y²=6

  Center=(5,0)

  Radius=36

  7.write the equation of the circle with center (0,-3) and radius of a 9 units

  X²+(y+3)²=81
• What is the center and radius of the circle define by the equation

  1.x²+y²+2x-4y-11=0

  Radius= 4

  Center=(-1,2)

  2.x²+y²-8x+4y-5=0

  Center= (4,-2)

  Radius=5

  3.x²+y²-6x-4y-3=0

  Center=(3,2)

  Radius=4