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What is the transformation of B(2 4) when dilated with a scale factor of ½ using the point (4 6) as the center of dilation?
When doing enlargements through a centre, the new position of any point is the distance of that point from the centre multiplied by the scale factor; it is easiest to treat the x- and y- coordinates separately.
To enlarge (2, 4) by a scale factor of ½ with (4, 6) as the centre of enlargement:
x: distance is (4 - 2) = 2 → new distance is 2 × ½ = 1 → new x is 2 + 1 = 3
y: distance is (6 - 4) = 2 → new distance is 2 × ½ = 1 → new y is 4 + 1 = 5
→ (2, 4) when enlarged by a scale factor of ½ with a centre of (4, 6) transforms to (3, 5).
What else can I help you with?
What is the transformation of C(9 3) when dilated by a scale factor of 3 using the origin as the center of dilation?
It is (27, 9).
Every dilation has a?
Center and Scale Factor....
What is the image of P for a dilation with center 0 0 and a scale factor of 2.5?
It is (2.5x, 2.5y) where P =(x,y).
What is the image of P for a dilation with center (0 0) and a scale factor of 2.5?
It is (2.5x, 2.5y) where P =(x,y).
Is a scale factor of 1 a dilation?
No a scale factor of 1 is not a dilation because, in a dilation it must remain the same shape, which it would, but the size must either enlarge or shrink.
What is the transformation of C(9 3) when dilated by a scale factor of 3 using the origin as the center of dilation?
It is (27, 9).
What is the transformation of B(4 8) when dilated by a scale factor of 2 using the origin as the center of dilation?
To find the transformation of point B(4, 8) when dilated by a scale factor of 2 using the origin as the center of dilation, you multiply each coordinate by the scale factor. Thus, the new coordinates will be B'(4 * 2, 8 * 2), which simplifies to B'(8, 16). Therefore, point B(4, 8) transforms to B'(8, 16) after the dilation.
How can you find the center of dilation of a triangle and its dilation?
To find the center of dilation of a triangle and its dilation, you can identify a pair of corresponding vertices from the original triangle and its dilated image. Draw lines connecting each original vertex to its corresponding dilated vertex; the point where these lines intersect is the center of dilation. The scale factor can be determined by measuring the distance from the center of dilation to a vertex of the original triangle and comparing it to the distance from the center to the corresponding vertex of the dilated triangle.
What is the transformation of C(9 3) when dilated with a scale factor of ⅓ using the point (3 6) as the center of dilation?
To find the transformation of the point C(9, 3) when dilated with a scale factor of ⅓ from the center of dilation (3, 6), you first subtract the center coordinates from C's coordinates: (9 - 3, 3 - 6) = (6, -3). Then multiply by the scale factor of ⅓: (6 * ⅓, -3 * ⅓) = (2, -1). Finally, add the center coordinates back: (2 + 3, -1 + 6) = (5, 5). Thus, the transformed point is (5, 5).
Triangle ABC below will be dilated with the origin as the center of dilation and scale factor of 1/2?
0.5
What are the invariant points of a dilation?
Invariant points of a dilation are the points that remain unchanged under the transformation. In a dilation centered at a point ( C ) with a scale factor ( k ), the invariant point is typically the center ( C ) itself. This means that when a point is dilated with respect to ( C ), it either moves closer to or further away from ( C ), but ( C ) does not move. Therefore, the only invariant point in a dilation is the center of dilation.
How do you solve dilation?
To solve a dilation problem, you first need to identify the center of dilation and the scale factor. The scale factor indicates how much larger or smaller the figure will be compared to the original. For each point on the original figure, you calculate the new coordinates by multiplying the distances from the center of dilation by the scale factor. Finally, plot the new points to create the dilated figure.
How do you graph a dilation?
To graph a dilation, first identify the center of dilation and the scale factor. For each point of the original figure, measure the distance from that point to the center of dilation, then multiply that distance by the scale factor to find the new distance from the center. Plot the new points at these distances, and connect them to form the dilated figure. Ensure that the orientation remains the same and that the shape is proportional to the original.
What is the transformation of c(93) when dilated by a scale factor of 3 using the origin as the center of dilation?
To dilate the point ( c(93) ) by a scale factor of 3 using the origin as the center of dilation, you multiply the coordinates of the point by 3. If ( c(93) ) refers to the point ( (9, 3) ), the transformed coordinates would be ( (9 \times 3, 3 \times 3) = (27, 9) ). Therefore, the transformed point after the dilation is ( c(27, 9) ).
What is called a transformation that shrinks or stretch a figure?
A transformation that shrinks or stretches a figure is called a dilation. In a dilation, all points of the figure are moved away from or toward a fixed center point, known as the center of dilation, by a scale factor. If the scale factor is greater than one, the figure is stretched; if it is between zero and one, the figure is shrunk.
What is A transformation that is determined by a center point and a scale factor?
A transformation determined by a center point and a scale factor is known as a dilation. In this transformation, all points in a geometric figure are moved away from or toward the center point by a factor of the scale. If the scale factor is greater than 1, the figure enlarges; if it is between 0 and 1, the figure shrinks. This transformation preserves the shape of the figure but alters its size.
What ia a transformation that shrinks or stretches a figure?
A transformation that shrinks or stretches a figure is known as a dilation. In a dilation, each point of the figure is moved away from or toward a fixed point called the center of dilation, by a scale factor. If the scale factor is greater than one, the figure is stretched; if it is between zero and one, the figure is shrunk. This transformation preserves the shape of the figure but alters its size.
