You use scale factor of 3/4 to create a dilated circle with a radius of 9 inches. What is the radius of the original circle?(1 point)
6 inches
To find the radius of the original circle, we can use the concept of dilation. Dilation is a type of transformation that changes the size of an object without changing its shape.
In this case, we are given that the dilated circle has a radius of 9 inches and a scale factor of 3/4. The scale factor represents how much the original object is scaled up or down.
To find the radius of the original circle, we can use the formula:
Original radius = Dilated radius / Scale factor
Substituting the given values:
Original radius = 9 inches / (3/4)
To divide by a fraction, we can multiply by its reciprocal:
Original radius = 9 inches * (4/3)
Multiplying the numbers:
Original radius = 36 inches / 3
Simplifying the division:
Original radius = 12 inches
Therefore, the radius of the original circle is 12 inches.
To find the radius of the original circle, we can use the formula:
Original radius = Scaled radius / Scale factor
Given:
Scaled radius = 9 inches
Scale factor = 3/4
Substituting the values into the formula:
Original radius = 9 inches / (3/4)
Original radius = 9 inches * (4/3)
Original radius = 36/3
Original radius = 12 inches
Therefore, the radius of the original circle is 12 inches.
Use the image to answer the question.
An illustration shows two triangles, one big and one small. In the small triangle, one side measures 11.4 inches and another side measures 18 inches. In the big triangle, the side corresponding to 11.4 inches in the small triangle measures x and the side corresponding to 18 inches measures 23.4 inches.
What is the length of x in decimal form to the nearest hundredth?
(1 point)