MATHEMATICS MIDDLE SCHOOL

Line segment AB has endpoints A(2, 9) and B(5, 8) . A dilation, centered at the origin, is applied to AB¯¯¯¯¯ . The image has endpoints A′(43, 6) and B′(103, 163) . What is the scale factor of this dilation? 32
23
2
3

Answers

Answer 1
Answer:

Answer:  The correct option is (B) (2)/(3).

Step-by-step explanation:  Given that the co-ordinates of the end-points of a line segment AB are A(2, 9) and B(5, 8). After being dilated about the origin (0, 0), the co-ordinates of the end-points of image A'B' are A^\prime\left((4)/(3),6\right) and B^\prime\left((10)/(3),(16)/(3)\right).

We are to find the scale factor of the dilation.

The scale factor of the dilation will be

S=\frac{\textup{length of the image line}}{\textup{length of the original line}}.

The lengths of the lines AB and A'B' are calculated using distance formula as follows:

AB=√((5-2)^2+(8-9)^2)=√(9+1)=√(10),\n\n\nA'B'=\sqrt{\left((10)/(3)-(4)/(3)\right)^2+\left((16)/(3)-6\right)^2\right)}=\sqrt{4+(4)/(9)}=\sqrt{(40)/(9)}=(2)/(3)√(10)~\textup{units}.

Therefore, the required scale factor of dilation is

S=(A'B')/(AB)=((2)/(3)√(10))/(√(10))=(2)/(3).

Thus, the scale factor of the dilation is (2)/(3).

Option (B) is CORRECT.
Answer 2
Answer: the answer is 2/3 
i took the test
hope this helps!

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