Which statement proves that the two circles are similar? (1 point)
1 answer:
Answer:
The circles B and D are similar because B can be mapped onto D by a translation of 8 units to the right and 1 unit down, followed by a dilation about its center by a scale factor of 0.5.
Step-by-step explanation:
If we translate the circle about its center, Circle B's center will coincide with Circle D's Center.
Circle B radius is 4 while Circle D radius is 2 so we need to dilate Circle B radius to shrink it to 2.
When we shrink a figure, the dilation scale factor must be less than 1 but what is the scale factor.
Use the formula
y=kx where y is the new radius and x is the original radius and k is the scale factor
THe second second statement is the answer.
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Answer:
(6, 9 ) and r = 3
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² - 12x - 18y + 108 = 0
Rearrange the x- terms and the y- terms together and subtract 108 from both sides, that is
x² - 12x + y² - 18y = - 108
To obtain standard form use the method of completing the square
add ( half the coefficient of the x and y terms )² to both sides
x² + 2(- 6)x + 36 + y² + 2(- 9)y + 81 = - 108 + 36 + 81
(x - 6)² + (y - 9)² = 9 ← in standard form
with centre = (6, 9 ) and r = = 3
<em><u>Look at the attached picture⤴</u></em>
<em><u>Hope it will help u....:)</u></em>
