Please Help me with some problems as soon as possible

rgeer

New member
Joined
Sep 14, 2005
Messages
32
1)If the dilation D (2,-4) = (-1,2), the scale factor k is equal to
K

a)-2
b)-1/2
c)1/2
d)2

2)If the area of trianle ANT is 5 square inches, the area of its image A'N'T' under the dilation D would be:
-2
a)5/2 square inches
b) 3 square inches
c) 10 square inches
D) 20 square inches

1)I believe it is A
2)I believe it is C

Also a few other problems,

3) Find the image of (6,-9) under the dilation D negative 1.
4) Find the image of (6,-9) under the dilation D 2/3-

For the above 2 problems:
3)I believe you would just multiply the -1 to 6 and then -9.
4)I believe you would just multiply the 2/3 to the 6 and then to the negative 9.

Apply this to the following problems: A blueprint has a scale of 1 inch=12 feet. Find the actual length represented by each length represented by each length of this blueprint.
5)3/4 inch
6)1 1/2 inches
7)2 1/8 inches

Im not sure how to do those but I think you have to change each of them to like units and multiply, so 3/4 times 12. Im not sure how to do those at all.

Apply this to the following problems: A blueprint has a scale of 1 inch=12 feet. Find the length on the blueprint needed to represent each length.

8)6 feet
9)24 feet

Thanks in advance for any help that anyone could give me.
Thanks again,
Ryan
 
G

Guest

Guest
Far to many to do in one go.....

1) D (2,-4) = (-1,2), scale factor K = ?

look at the first x point(2) and the second x point(-1).....what do you muliply (-1) by to equal (2). This is the scale factor. Check by doing the same to the y values. It will give the same scale factor result.


2)
 

Gene

Senior Member
Joined
Oct 8, 2003
Messages
1,904
1) The scale factor is what you multiply the first by to get the second.
2*k= -1
-4*k=2
Solve for k.

2) It ANT is a right triangle with AT the hypotenuse then
A'N' => -2AN
T'N' => -2TN
The area of ANT is 1/2 * AN*TN = 5
What is the area of A'N'T'?

3) & 4) correct.

5-7) Usually that would be the way to do it, but if you use a scale factor k = (12 feet)/(1 inch) k will take care of the change of units.
(3/4) inch * (12 feet/1 inch) = (3/4)*(12/1) feet

For the other two the scale factor becomes (1 inch)/(12 feet)

EDITED: There seems to be some doubt about which is the source and which is the result in your notation
D (a,b) = (c,d)
I asumed a,b becomes c,d
APM thinks it goes the other way. I dunno.
 

rgeer

New member
Joined
Sep 14, 2005
Messages
32
Gene said:
1) The scale factor is what you multiply the first by to get the second.
2*k= -1
-4*k=2
Solve for k.

2) It ANT is a right triangle with AT the hypotenuse then
A'N' => -2AN
T'N' => -2TN
The area of ANT is 1/2 * AN*TN = 5
What is the area of A'N'T'?

3) & 4) correct.

5-7) Usually that would be the way to do it, but if you use a scale factor k = (12 feet)/(1 inch) k will take care of the change of units.
(3/4) inch * (12 feet/1 inch) = (3/4)*(12/1) feet

For the other two the scale factor becomes (1 inch)/(12 feet)

EDITED: There seems to be some doubt about which is the source and which is the result in your notation
D (a,b) = (c,d)
I asumed a,b becomes c,d
APM thinks it goes the other way. I dunno.
1)-2 I believe is the answer, Am I correct?
2)10 square inches I believe, Am I correct?
3) (-6,9), am I correct?
4) (4,-6) am I correct?
5) 9, am I correct?
6)18, am I correct?
7)25.5, am I correct?
8) I still dont know
9) Dont know

If anyone could help me out, that would be great
Ryan
 

Gene

Senior Member
Joined
Oct 8, 2003
Messages
1,904
Since you are quoting me...
It does depend on which way you are going. If you are going from a house to a blueprint k might be 1 inch/12 feet. A blueprint to a house would be 12 feet/1 inch. I told you I didn't know what
D (2,-4) = (-1,2)
meant. I think it is
(2,-4) => (-1,2)
so I said
2*k=-1
How did you get -2 from that??? I get -1/2
But you may want to hear from APM again since you took his answer.

2) (1/2)*AN*AT = 5
AN*AT=10

(1/2)(-2*AN)*(-2*AT) =
(1/2)*4(AN*AT) =
(1/2)*4*(10) =
20
(BTW Area is always as the square of the scale factor. Volume is as the cube.)

3&4) still correct
5&6&7) correct
8) 6 feet* 1 inch/12 feet = 1/2 inch

9) 24 feet* 1 inch/12 feet = 2 inches
 
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