Question

1)Circle 1 is centered at (−4, 5)(−4, 5) and has a radius of 2 centimeters. Circle 2 is centered at (2, 1)(2, 1) and has a radius of 6 centimeters.
What transformations can be applied to Circle 1 to prove that the circles are similar?
Enter your answers in the boxes.

The circles are similar because you can translate Circle 1 using the transformation rule (, ) and then dilate it using a scale factor of .

2)The sector of a circle with a 12-inch radius has a central angle measure of 60°.
What is the exact area of the sector in terms of ​ π ​?

Answer 1

Figures of same shape and size are similar .Two circles  C1&C2 will be similar.

Circle 1 has a center of (-4,5) and circle 2 has a center of (2,1) .The x of the center is having the translation x+6 and the y  is having a translation of y-4.The center of the circle is dilated by 3 units.

The circles are similar because you can translate Circle 1 using the transformation rule (x+6,y-4 ) and then dilate it using a scale factor of 3.

2) Area of sector = $\pi.r^{2}\alpha$÷360.

Where α is the angle made at center.

Area of given sector= π(12)(12)(60)÷360 =24π.