Line segment has endpoints of A(1,4) and B(-2,1), It is dilated and A’(3,12) and B(-6,3). What is the scale factor?
Triangle ABC has vertices A(0,3), B(3,6), and C(12,18). It is dilated with a scale factor of ⅓. Give the new vertices A’, B’, C’ using ordered pairs (x,y) form
If you would like to dilate a square with a side length of 8 units to create a square with a side length of 10 units, what scale factor should you use? Write your answer in decimal form.
Used a Scale factor of ⅔ to dilate a circle with radius of 18cm. What is radius or original circle?
A rectangle with w=2 and l=4 is similar to rectangle with length of 1. What is width of similar rectangle? (simplified fraction)
For the first question:
To find the scale factor, you can use the formula:
Scale factor = (New length)/(Original length)
The original length of the line segment AB is:
Length AB = sqrt((1-(-2))^2 + (4-1)^2)
= sqrt(3^2 + 3^2)
= sqrt(18)
The new length of the line segment A'B' is:
Length A'B' = sqrt((3-(-6))^2 + (12-3)^2)
= sqrt(9^2 + 9^2)
= sqrt(162)
Therefore, the scale factor is:
Scale factor = Length A'B' / Length AB
= sqrt(162) / sqrt(18)
= (sqrt(9) * sqrt(18)) / sqrt(18)
= sqrt(9)
= 3
The scale factor is 3.
For the second question:
To find the new vertices A', B', and C', you can multiply the coordinates of each vertex by the scale factor of 1/3.
A' = (0,3) * 1/3 = (0*1/3, 3*1/3) = (0,1)
B' = (3,6) * 1/3 = (3*1/3, 6*1/3) = (1,2)
C' = (12,18) * 1/3 = (12*1/3, 18*1/3) = (4,6)
The new vertices are A'(0,1), B'(1,2), and C'(4,6).
For the third question:
To find the scale factor, you can use the formula:
Scale factor = (New side length)/(Original side length)
The original side length of the square is 8 units.
The new side length of the square is 10 units.
Therefore, the scale factor is:
Scale factor = 10/8
= 1.25
The scale factor is 1.25.
For the fourth question:
To find the radius of the original circle, you can use the formula:
Radius of original circle = (Radius of dilated circle) / Scale factor
Radius of dilated circle = 18 cm
Scale factor = 2/3
Therefore, the radius of the original circle is:
Radius of original circle = 18 cm / (2/3)
= 18 cm * (3/2)
= 27 cm
The radius of the original circle is 27 cm.
For the fifth question:
To find the width of the similar rectangle, you can use the formula:
Width of similar rectangle = (Width of original rectangle) * Scale factor
Width of original rectangle = 2
Scale factor = 1
Therefore, the width of the similar rectangle is:
Width of similar rectangle = 2 * 1
= 2
The width of the similar rectangle is 2.
i just need the aswers
Apologies for the confusion. Here are the answers:
1. The scale factor is 3.
2. The new vertices are A' (0,1), B' (1,2), and C' (4,6).
3. The scale factor is 1.25.
4. The radius of the original circle is 27 cm.
5. The width of the similar rectangle is 2.