2a 7 = 3a + 10 vertical s are . how do you find the center of this circle? the center of a circle...
DESCRIPTION
Definition of Linear pair– 2 angles that are adjacent and supplementary 2x x – 84 = 180TRANSCRIPT
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2a - 7 3a + 10
2a – 7 = 3a + 10
Vertical <‘s are ≅
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(3,8)
(4,-1)
How do you find the center of this circle?
218,
243 The center of a
circle is the midpoint of any
diameter.
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2x + 8 6 x - 84
Definition of Linear pair– 2 angles that are adjacent and supplementary
2x + 8 + 6x – 84 = 180
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2x + 184x
Definition of perp. lines - 2 lines that intersect to form a right angle
Definition of complementary <‘s - 2 angles whose sum = 90 degrees
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AB is on a number line. Explain how to find its midpoint.
A + B 2A _____ has no size, no
dimensions, just position.
Point
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Write the standard equation of a circle.
(x – h )² + (y – k )² = r²
Simplify √175
5√7
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3x + 20
8x - 5
Solve for x. Explain your answer.
3x + 20 = 8x – 5
vertical angles are congruent
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__________ is the set of all points.
Space
4 _____ points determine space.
noncoplanar
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The midpoint of GD is (4,-5) and the coordinates of D are (-3,1). Find the coordinates of G.
___________________________________G M D(4, -5) (-3,1)
Double the midpoint and do the opposite of the given endpoint.
Step 1 --(8,-10)
Step 2---(+3,-1)
Answer (11,-11)
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• What is the easiest way to prove a quad is a parallelogram?
• If the midpoints of the diagonals are the same.
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What postulate is demonstrated here?
The intersection of 2 planes is a line.
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• (2,5);(7,5);(-4,5)
• Points on the same line because all the y-coordinates are the same.
• y = 5
• Horizontal line
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(3,2), ( 3, -1), (3, 7)
Points on the same line because all the x’s are the same
Vertical line
X=3
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• What is a conjecture?
• A conclusion you reach using inductive reasoning.
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1.Write the Circle Equation
X ² + y² = 4
Center (0,0)
Radius = 2
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A B
CD
E F
GH
Are the following points collinear, coplanar, or noncoplanar? (Why?)
H, G, C
Coplanar
Any 3 pts lie in a plane
F,B,E,A
Coplanar – ll lines
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A B
CD
E F
GH D,C,E,H
Noncoplanar
Skew lines
Are the following points collinear, coplanar,
or noncoplanar? (Why?)
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Points that are in space are ___________points.
Noncoplanar
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•If a circle has a center (4,-5) and it is tangent to the y- axis, what would its equation look like?
(X-4)² + (y+5)²= 16
Radius = 4 (distance from y-axis)
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•Write the equation of a circle for a circle with an area = 121 π and a center ( -10, 4).
(X+10)² + (y-4)² = 121
121π = πr²
121 = r²
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M R P-26 -2
If R is the midpt of MP findMR=_____ RP=_____and the coordinate of R.
MP = -2 - -26 =24
MR = RP = 12 Def of midpt.
Coordinate of R = -2 – 12 = 14 or -26 + 12 = -14
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(-2,7) (-2,-3)
Find the center of the above circle-which is the midpt. of the diameter.
(-2,2)
Find the radius of the above circle.r = 5
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H E Y2X 5X-14 21
Write an equation.
7X = 35
X = 5
Name the postulate you used to write the above equation.
Segment Addition Postulate
Find the coordinate of E.
21- 25 = -4
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• Find the midpoint of AB if you are on a number line .
• A+B• 2• If you are • in a plane.
x₁ + x₂ , y₁ + y₂ 2 2( )