Mathematics, 19.07.2019 06:30 user434568

Very confused ! circle 1 is centered at (5,8) and has a radius of 8 centimeters. circle 2 is centered at (1,−2) and has a radius of 4 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 ( _ ) .

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We know that
Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.
In this problem to prove circle 1 and circle 2 are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.

we have that
Circle 1 is centered at (5,8) and has a radius of 8 centimeters
Circle 2 is centered at (1,-2) and has a radius of 4 centimeters

step 1
Move the center of the circle 1 onto the center of the circle 2
the transformation has the following rule
(x,y)> (x-4,y-10)
so
(5,8)> (5-4,8-10)> (1,-2)
so
center circle 1 is now equal to center circle 2
The circles are now concentric (they have the same center)

step 2
A dilation is needed to decrease the size of circle 1 to coincide with circle 2

scale factor=radius circle 2/radius circle 1> 4/8> 0.5

radius circle 1 will be=8*scale factor> 8*0.5> 4 cm
radius circle 1 is now equal to radius circle 2

A translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similar

the answer is
The circles are similar because you can translate Circle 1 using the transformation rule (x-4,y-10) and then dilate it using a scale factor of (0.5)

Answer from: Quest

4 + 5 7/9= 9 7/9

step-by-step explanation:

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

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Very confused ! circle 1 is centered at (5,8) and has a radius of 8 centimeters. circle 2 is center...

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