#### rgeer

##### New member
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
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
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
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