Circle 1 has center (−4, −7) and a radius of 12 cm. Circle 2 has center (3, 4) and a radius of 15 cm.
2 answers:
<h3>Answer with explanation:</h3>
It is given that:
Circle 1 has center (−4, −7) and a radius of 12 cm.
Circle 2 has center (3, 4) and a radius of 15 cm.
Two circles are said to be similar if by some translation and dilation it could be placed over the other to form the same circle.
The circles are similar because the transformation rule ( x,y ) → (x+7,y+11) can be applied to Circle 1 and then dilate it using a scale factor of 5/4
( Since, as the center of circle 1 is (-4,-7)
so,
(-4+7,-7+11) → (3,4)
( Since, the radius of circle 1 is 12 and that of circle 2 is 15 cm.
so, let the scale factor be k .
that means :
)
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Answer:
The ordered pairs represent points on the line are
(4, 3) ⇒ C
(2, ) ⇒ D
(-8, -6) ⇒ E
Step-by-step explanation:
To find the ordered pairs represent points on the line, substitute x by the x-coordinate of each point, if the value of y equals the y-coordinate of the point, then the point is on the line.
∵ The equation is y = x
∵ The ordered pair is (8, )
→ Substitute x by 8
∴ y = (8)
∴ y = 6
∵ The value of y does not equal the y-coordinate of the ordered pair
∴ The ordered pair (8, ) does not represent a point on the line
∵ The ordered pair is (,
)
→ Substitute x by
∴ y = (
)
∴ y =
∵ The value of y does not equal the y-coordinate of the ordered pair
∴ The ordered pair (,
) does not represent a point on the line
∵ The ordered pair is (4, 3 )
→ Substitute x by 4
∴ y = (4)
∴ y = 3
∵ The value of y equal the y-coordinate of the ordered pair
∴ The ordered pair (4, 3) represents a point on the line
∵ The ordered pair is (2, )
→ Substitute x by 2
∴ y = (2)
∴ y =
∵ The value of y equal the y-coordinate of the ordered pair
∴ The ordered pair (2, ) represents a point on the line
∵ The ordered pair is (-8, -6 )
→ Substitute x by -8
∴ y = (-8)
∴ y = -6
∵ The value of y equal the y-coordinate of the ordered pair
∴ The ordered pair (-8, -6) represents a point on the line