Circle P
has center
P
(2, 0) and radius 20. Circle
Q
has center
Q
(0, 4) and radius 2.
(a)
Describe the rule for translating center
Q
onto center
P
.
(b)
Determine the scale factor for dilating circle
Q
so that it has the same radius as circle
P.
(c)
Are circles
P
and
Q
similar? Explain your answer.

Answers

Answer 1

Answer: Siras ! Don't try to picture this all in your head !
You'll wear out your brain.
You MUST sketch it on a piece of paper.
Draw an x-axis and a y-axis, then draw the two circles.

I'm drawing myself a picture right now, and I'm
supposed to be some kind of a genius.

a). In order to move Circle-Q so that both centers are
at the same point, you need to move the center of Q
4 units down and 2 units to the right.
      When you do that, you'll have the little circle inside the
big circle, with their centers both at the same place.

b). The radius of Q is 2.
   The radius of P is 20.
   What do you have to multiply 2 by, in order to get 20 ?
   THAT's the scale factor to dilate Q so that it has the same
radius as P.
   When you do that, suddenly it'll look like you only have one circle
on the paper ... they'll both have the same radius and their centers are
at the same place, so you can't tell them apart.

c). All circles are similar !

I went online (you could easily go there too). I searched the question
"Are circles similar ?" and a lot of interesting stuff came up. (you could
do that too). I saw a lot of ways to prove that all circles are similar.
The best one says:

   Two figures are "similar" if you can make one of them
   exactly fit on top of the other one (make them congruent)
   with translations and dilations.

You just did that with P and Q !

-- Translation is moving them around.
   You moved Q and put the centers of both circles at the same place.

-- Dilation is blowing it up or blowing it down, so its size changes
but its shape doesn't change.
   You blew Q up so that it had the same radius as P.
   Then the two circles exactly fit over/under each other.

So the two circles are similar.

Related Questions

What substitution should be used to rewrite 6(x + 5)2 + 5(x + 5) – 4 = 0 as a quadratic equation? u = (x + 5) u = (x – 5) u = (x + 5)2 u = (x – 5)2
48 pk. 6 qt. divided by 6
Julie just doesn't get how fraction division works .None of it makes sense she whined to Scott one day why does 3 over 4 divide by 2 equals to 3 over 8?
A swimming pool is 20 meters long and 12 meters wide the bottom of the pool is slanted so that the water depth is 1.3 at theshallow end and 4 meters deep at the deep end find the angle of depression of the bottom of the pool
For the data in the table, does y vary directly with x? If it does, write an equation for the direct variationx y10 1215 1820 24

The maximum weight allowed per car on The Wildcat carnival ride is 221 pounds. Your friend weighs 60 pounds. To be able to ride in a car together, how much can you weigh? Write and solve an inequality.(1 point)x – 60 inequality-lessthanorequalto 221; at most 60 pounds
x + 60 inequality-lessthanorequalto 221; at most 161 pounds
x + 161 inequality-lessthanorequalto 221; at most 60 pounds
x + 60 inequality-lessthanorequalto 161; at most 221 pounds

Answers

given that the max. weght per car is 221 pounds
- my friend weighs 60 pounds
- let my weight x

so than will get the inequality

x+60 <= 221

x <= 221-60

x <= 161

Answer:

x + 60 < 221; at most 161 pounds.

Step-by-step explanation:

your welcome :)

How to factor a quadratic equation y=-2x^2+8x-6

Answers

first factor out that -2
y=-2(x^2-4x+3)
what 2 number muitply to 3 and add to -4
-1 and -3
y=-2(x-3)(x-1)

Work out 5/8 of 10 litres

Answers

5/8 of 10 litres is 6.25 litre
because 5/8=0,625
0,625 * 10 = 6,25 :))

8a2 + 6a = 5
how do I do this?

Answers

$8a^2 + 6a = 5 \n \n8a^2 + 6a -5 =0\n \n\Delta = b^(2)-4ac = 6^(2)-4*8* (-5)=36 +160=196\n \na_(1)=(-b-√(\Delta ))/(2a) =(-6- √(196))/(2*8)=(-6- 14)/(16)= (-20)/(16)=- (5)/(4)=-1(1)/(4)\n \na_(2)=(-b+√(\Delta ))/(2a) =(-6+√(196))/(2*8)=(-6+14)/(16)= (8)/(16)= (1)/(2)$

15-1.5/d in word phrases

Answers

fifteen minus the quotient of one point 5 divided by a number

15 subtract the quotient of 1.5 and d.

How many 2 inch cubes are needed to completely fill a cubic box of edges 8 inches?

Answers

64 of them because 2 inch cubes are needed to completely fill a cubic box of edges 8 inches

Hope I Helped You!!! :-)

Have A Good Day!!!

Other Questions

Find the common ratio of the geometric sequence: 4,3,9/4

the measures of an exterior angle and the adjacent interior angle add p to 360 because they form a linear plane?

What is the greatest possible error if Irina measured the weight of her dog as 13 pounds?0.1 pounds 0.5 pounds 12.5 pounds 13.5 pounds

8 m15 mWhat is the perimeter?