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Enlarge shape A with a scale factor of -½ centre O whats this mean - especially the centre 0?
Wiki User
∙ 13y ago
When enlarging a shape through a centre (O in this case, which is the usual letter of the origin for x/y axes) measure the distance from each point on the shape to the centre of enlargement, multiply it by the scale factor to get the new distance and then (keeping the measuring device, eg ruler, still) measure the new distance from the centre.
By having a scale factor the exact size of the image is known; and
by having a centre of enlargement the exact position of the image is known.
Note: When the scale factor is negative, the distances will change sign and so be measured in the opposite direction.
So in this case, the following will happen:
. . . . . . . . . . . . . . . . . . . . . .
. . . ./\ . . . . . . . . . . . . . . . . .
. . . / .\. . . . . . . . . . . . . . . . .
. . ./__\ . . . . . .O . . . \ . . ./. .
. . / . . .\. . . . . . .* . . . \--/. .
. ./. . . . \ . . . . . . . . . . .\/ . . .
. / . . . . .\. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .
Where the A shape on the left becomes the (smaller) upside down A on the right when enlarged with a scale factor of -½ and centre O.
(You'll have to excuse the ASCII graphics for not complete accuracy.)
Wiki User
∙ 13y ago
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A transformation that proportionally reduces or enlarges a figure?
Scaling will proportionally reduce or enlarge a figure. The amount of scaling is given by the scale factor (greater than zero) If the scale factor is less than 1, the figure is reduced and it is sometimes called a contraction If the scale factor is greater than 1, the figure is enlarged, and it is called a dilation or enlargement. If a centre of enlargement is used, the distance of every point from the centre is multiplied by the scale factor. The scale factor can be negative in which case the distance to the new point is measured on the opposite side of the centre to the original point.
When dilating a triangle to enlarge the triangle you must use a scale factor that is 1 1 equals 1 equals 0?
No, there cannot be a zero in any scale factor.
Transformation that enlarges or reduces a figure?
Scaling changes the size of a figure. If the scale factor is greater than 1, the figure is enlarged; if the scale factor is less than 1, the figure is reduced. I the scale factor is equal to 1, the figure's size is unchanged. If there is a centre of enlargement, the new figure can be drawn exactly by multiplying the distance of every point from the centre of enlargement, multiplying this by the scale factor and drawing the new point at this distance from the centre of enlargement. (For a polygonal figure, only the vertices need be measured and the lines between the vertices of the original figure drawn in). With a centre of enlargement, the scale factor can be negative. In this case, the distance to the new points is measured on the opposite side of the centre to the original points, so that it is a straight line form the original point, through the centre to the new point.
What is the relationship between the vertices of a shape the scale factor and the center of dilation?
None. The vertices, the scale factor as well as the centre of dilation can each be defined independently of the other two. Each different combination will result in a different image.
How do you enlarge a shape with a sf?
Redraw the same shape with multiplying each length of the shape by the scale factor.If you are enlarging through a centre of enlargement, measure the distance from each point (vertex) to the centre and continuing on a straight line through the centre, measure that distance multiplied by the scale factor and plot the point there, drawing in the lines of the shape.When doing this on squared paper, the measurement of the distance can often be easily done by counting the squares horizontally and vertically from the point to the centre, and count each of these values multiplied by the scale factor on the other side of the centre point.For example, a point (1, 0) enlarged by a scale factor of 2 through the centre (2, 3) would be plotted at:Horizontal distance is 2 - 1 = 1 squares, times 2 = 2 squares horizontally beyond (2, 3) which makes the new x co-ordinate 2 + 2 = 4Vertical distance is 3 - 0 = 3 squares, times 2 = 6 squares vertically beyond (2, 3) which makes the new y co-ordinate 3 + 6 = 9Making (1, 0) → (4, 9)
How do you use the scale factor of a triangle to enlarge it?
The way you use a scale factor to enlarge a triangle is to multiply each side of the triangle by that scale factor. Your triangle will then be that many times larger.
A transformation that proportionally reduces or enlarges a figure?
Scaling will proportionally reduce or enlarge a figure. The amount of scaling is given by the scale factor (greater than zero) If the scale factor is less than 1, the figure is reduced and it is sometimes called a contraction If the scale factor is greater than 1, the figure is enlarged, and it is called a dilation or enlargement. If a centre of enlargement is used, the distance of every point from the centre is multiplied by the scale factor. The scale factor can be negative in which case the distance to the new point is measured on the opposite side of the centre to the original point.
A triangle with a vertex at A(4 -8) is dilated so that A' has coordinates (-3 6). The scale factor used was?
It depends where the centre of enlargement (dilation) was; it can be any value.As all you have given us is the change in the coordinate of the A vertex, so all we can conclude is that the centre of enlargement is somewhere along the line y + 2x = 0.Examples:If the centre is at (3, -6) then the scale factor is -6If the centre is at (0.5, -1) then the scale factor is -1If the centre is at (0, 0) then the scale factor is -3/4If the centre is at (-3, 6) then the scale factor is 0If the centre is at (-4, 8) then the scale factor is 1/8If the centre is at (-10, 20) then the scale factor is 1/2If the centre is at (11, -22) then the scale factor is 2If the centre is at (1.4, -2.8) then the scale factor is 6(As the centre tends towards ±∞ the scale factor tends towards 1 [from below towards -∞, from above towards +∞].)
What does enlarge by a scale factor of 2 mean?
times by two
The ratio used to enlarge or reduced similar figures?
Scale Factor
What scale factor would you use to enlarge a 4 by 6 into an 18 times 27 photo?
a scale factor of 4.5 is your answer
What is a negative scale factor?
A negative scale factor is used to produce the image on the other side of the centre of enlargement (scaled to the absolute value of the scale factor).
When dilating a triangle to enlarge the triangle you must use a scale factor that is 1 1 equals 1 equals 0?
No, there cannot be a zero in any scale factor.
How do you enlarge a shape using a scale factore of 0.5?
When a shape is enlarged, the scale factor tells by how much to multiply each length of the original shape to get the corresponding length on the new shape. So with a scale factor for 0.5 (or 1/2), each length of the new shape is 0.5 (or 1/2) times the lengths of the original shape. For example, to enlarge a triangle with sides 6", 8", 10" by a scale factor or 0.5, the lengths become 6" x 0.5 = 3", 8" x 0.5 = 4", 10" x 0.5 = 5"; so the resulting triangle has sides 3", 4", 5". To do the enlargement through a centre of enlargement, a straight line is drawn from each point (vertex) of the shape to the centre of enlargement. The distance from the centre to the point is measured and multiplied by the scale factor; this new distance is measured along the same line from the centre of enlargement as the original point. In this case, negative scale factors can be given, in which case the new distance is measured in the opposite direction from the centre of enlargement, away from the original point.
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.
How does scale factor affect length and angle measure?
Scale factor can enlarge or decrease SIDE lengths, however, angle measurements will not change. Scaling creates similar figures.
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 = 3y: 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).
