Study Online Dilation Introduction:
Dilation is a change (notation Dk) that produces a picture that is the same shape as the original, but is a different size. Dilation stretches or shrinks the original diagram.
The explanation of dilation contains the ratio or scale factor and the middle of the dilation. The middle of dilation is a set point in the plane about which every point are expanded or contracted. It is the just invariant point under dilation.
A dilation of scalar factor k whose middle of dilation is the basis written by: Dk (x, y) = (kx, ky). If the scale factor, k, is larger than 1, the picture is an enlargement.
If the scale factor is 0 to 1, the picture is a reduction.
Study Online Dilation - Definition:
A dilation is a vary of the plane, Dk, such that if O is a set point, k is a non-zero real number, and P' is the picture of point P, then O, P and P' are collinear and `(OP ' )/(OP)` = k.
Notation: Dk(x, y) = (kx, ky )
Examples for Study online Dilation:
Study online Dilation - Example 1:
PROBLEM:
Sketch the dilation picture of triangle ABC with the middle of dilation at the origin and a scale factor of 2.
Examine: Notice how EACH coordinate of the triangle has been multiplied by the scale factor (x2).
Study online Dilation - Example 2:
PROBLEM:
Sketch the dilation picture of pentagon ABCDE with the middle of dilation at the origin and a scale factor of 1/3.
Examine: Notice how EACH coordinate of the pentagon has been multiply the scale factor (1/3).
Note: Multiplying by 1/3 is the same as dividing by 3!
Study online Dilation - Example 3:
PROBLEM:
Sketch the dilation diagram of rectangle EFGH with the middle of dilation at point E and a scale factor of 1/2.
Examine:
E and its picture are the same. It is main to observe the distance from the middle of the dilation, E, to the other points of the diagram. Notice EF = 6 and E'F' = 3.
Note:
Be sure to measure distances for this problem.
Dilation is a change (notation Dk) that produces a picture that is the same shape as the original, but is a different size. Dilation stretches or shrinks the original diagram.
The explanation of dilation contains the ratio or scale factor and the middle of the dilation. The middle of dilation is a set point in the plane about which every point are expanded or contracted. It is the just invariant point under dilation.
A dilation of scalar factor k whose middle of dilation is the basis written by: Dk (x, y) = (kx, ky). If the scale factor, k, is larger than 1, the picture is an enlargement.
If the scale factor is 0 to 1, the picture is a reduction.
Study Online Dilation - Definition:
A dilation is a vary of the plane, Dk, such that if O is a set point, k is a non-zero real number, and P' is the picture of point P, then O, P and P' are collinear and `(OP ' )/(OP)` = k.
Notation: Dk(x, y) = (kx, ky )
Examples for Study online Dilation:
Study online Dilation - Example 1:
PROBLEM:
Sketch the dilation picture of triangle ABC with the middle of dilation at the origin and a scale factor of 2.
Examine: Notice how EACH coordinate of the triangle has been multiplied by the scale factor (x2).
Study online Dilation - Example 2:
PROBLEM:
Sketch the dilation picture of pentagon ABCDE with the middle of dilation at the origin and a scale factor of 1/3.
Examine: Notice how EACH coordinate of the pentagon has been multiply the scale factor (1/3).
Note: Multiplying by 1/3 is the same as dividing by 3!
Study online Dilation - Example 3:
PROBLEM:
Sketch the dilation diagram of rectangle EFGH with the middle of dilation at point E and a scale factor of 1/2.
Examine:
E and its picture are the same. It is main to observe the distance from the middle of the dilation, E, to the other points of the diagram. Notice EF = 6 and E'F' = 3.
Note:
Be sure to measure distances for this problem.
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