Circles c and c are similar state the translation rule and the scale factor of dilation

Mathematics

1 answer:

IrinaVladis [17]3 years ago

5 0

Answer:

To find the scale factor for a dilation, we find the center point of dilation and measure the distance from this center point to a point on the preimage and also the distance from the center point to a point on the image.

Step-by-step explanation:

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write the x and y coordinate (in the second and third column, respectively) of dilation of quadrilateral ABCD with vertices A(1,

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The coordinates of the dillated vertices are $A'(x,y) = (2,2)$ , $B'(x,y) = (4,4)$ , $C'(x,y) = (8,2)$ and $D'(x,y) = (4,-2)$ .

Step-by-step explanation:

From Linear Algebra, we define dilation by the following equation:

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation, dimensionless.

$P(x,y)$ - Original point, dimensionless.

$k$ - Scale factor, dimensionless.

$P'(x,y)$ - Dilated point, dimensionless.

If we know that $O(x,y) = (0, 0)$ , $k = 2$ , $A(x,y) = (1,1)$ , $B(x,y) = (2,2)$ , $C(x,y) = (4,1)$ and $D(x,y) = (2,-1)$ , then the dilated points are, respectively: