Find the new triangle that undergoes a scale factor of 2.5 and a center of dilation at the origin.
A(-2,-2)
C(0,0)
B(2,-4)
Xmin:
-10
Xmax:
10
Ymin:
-10
Ymax:
10
To find the new coordinates of each point after a scale factor of 2.5 and a center of dilation at the origin, we can multiply each coordinate by the scale factor.
A' = (-2 * 2.5, -2 * 2.5) = (-5, -5)
C' = (0, 0) (The center of dilation remains the same)
B' = (2 * 2.5, -4 * 2.5) = (5, -10)
The new triangle after the dilation is formed by the points A'(-5, -5), C'(0, 0), and B'(5, -10).
Find the new triangle that undergoes a scale factor of 1/2 and a center of dilation at the origin
A(-8,-4)
C(2,8)
B(10,-6)
Xmin:
-10
Xmax:
10
Ymin:
-10
Ymax:
10
To find the new coordinates of each point after a scale factor of 1/2 (or 0.5) and a center of dilation at the origin, we can multiply each coordinate by the scale factor.
A' = (-8 * 0.5, -4 * 0.5) = (-4, -2)
C' = (2 * 0.5, 8 * 0.5) = (1, 4)
B' = (10 * 0.5, -6 * 0.5) = (5, -3)
The new triangle after the dilation is formed by the points A'(-4, -2), C'(1, 4), and B'(5, -3).
Using the lengths of the sides, find the scale factor:
Goes from ABCD to EFGH:
Goes from EFGH to ABCD:
A(-10,6)
B(-10,-2)
C(-6,-2)
D(-6,6)
E(-5,3)
F(-5,-1)
G(-3-1)
H(-3,3)
Xmin:
-10
Xmax:
10
Ymin:
-10
Ymax:
10
To find the scale factor, we can compare the lengths of corresponding sides between the two triangles.
AB = √((-10 - (-10))^2 + (-2 - 6)^2) = √(0^2 + (-8)^2) = 8
EF = √((-5 - (-5))^2 + (-1 - 3)^2) = √(0^2 + (-4)^2) = 4
BC = √((-10 - (-6))^2 + (-2 - (-2))^2) = √((-4)^2 + 0^2) = 4
FG = √((-5 - (-3))^2 + (-1 - (-1))^2) = √((-2)^2 + 0^2) = 2
CD = √((-6 - (-6))^2 + (6 - (-2))^2) = √(0^2 + 8^2) = 8
GH = √((-3 - (-3))^2 + (3 - (-1))^2) = √(0^2 + 4^2) = 4
DA = √((-6 - (-10))^2 + (6 - 6)^2) = √((-4)^2 + 0^2) = 4
HE = √((-3 - (-5))^2 + (3 - 3)^2) = √((-2)^2 + 0^2) = 2
The scale factor from ABCD to EFGH can be determined by comparing the lengths of corresponding sides:
Scale factor: EF / AB = 4 / 8 = 0.5
The scale factor from EFGH to ABCD can be determined by comparing the lengths of corresponding sides:
Scale factor: AB / EF = 8 / 4 = 2
Therefore, the scale factor from ABCD to EFGH is 0.5, and the scale factor from EFGH to ABCD is 2.
The hypotenuse of a triangle was 20 cm and the hypotenuse of the final triangle was 13.0 cm. What is the scale factor?
To find the scale factor, we can compare the lengths of corresponding sides between the two triangles.
Let's assume the original triangle had sides of length a, b, and c, where c represents the hypotenuse.
Using the Pythagorean theorem, we know that a^2 + b^2 = c^2.
In the original triangle, we have a^2 + b^2 = 20^2.
Now, let's assume the final triangle has sides of length ka, kb, and kc, where k is the scale factor and ka, kb, and kc represent the corresponding sides of the final triangle.
Using the Pythagorean theorem again, we have (ka)^2 + (kb)^2 = (kc)^2.
Simplifying, we get (k^2)(a^2 + b^2) = (kc)^2.
Substituting a^2 + b^2 = 20^2, we have (k^2)(20^2) = (kc)^2.
Simplifying further, (k^2) = (kc)^2 / (20^2) = (13^2) / (20^2).
Taking the square root of both sides, we get k = 13 / 20 = 0.65.
Therefore, the scale factor is 0.65.
The diameter of a circle was 11 cm and the diameter of the final circle was 33 cm.
To find the scale factor, we can compare the lengths of corresponding sides between the two circles. Since the diameter of a circle is twice the length of its radius, the scale factor can be found by comparing the radii of the two circles.
Let r1 represent the radius of the original circle with a diameter of 11 cm, and r2 represent the radius of the final circle with a diameter of 33 cm.
Using the formula for the radius of a circle, we have r1 = 11 cm / 2 = 5.5 cm and r2 = 33 cm / 2 = 16.5 cm.
The scale factor can be found by dividing the radius of the final circle by the radius of the original circle:
Scale factor = r2 / r1 = 16.5 cm / 5.5 cm = 3.
Therefore, the scale factor is 3.
The two equilateral triangles below are similar (but not drawn to scale). What is the scale factor?
16 inches.
46.4 inches.
The scale factor to go from the triangle on the left to the triangle on the right is