Question

Triangle ABC has vertices A(5, 3) , B(3, 7) , and C(1, 4) . Triangle ABC is dilated, and the vertices of the image are A′(2.5, 1.5) , B′(1.5, 3.5) , and C′(0.5, 2) . The center of dilation is the origin.

What is the scale factor of the dilation?


0.25

0.5

2

4

Answer 1

I believe the answer would be 0.5

Hope this helps ;}

Answer 2

Answer: The correct answer is (B) 0.5.

Step-by-step explanation: Given that A(5, 3) , B(3, 7) and C(1, 4) are the vertices of ΔABC and A′(2.5, 1.5) , B′(1.5, 3.5) and C′(0.5, 2) are the vertices of ΔA'B'C'.

We are to find the scale factor of the dilation of the centre of dilation is origin.

We know that the scale factor of dilation is given by the following formula:

`S_c=\frac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.`

We can calculate the lengths of the corresponding sides AB and A'B' of ΔABC and ΔA'B'C' respectively using distance formula as follows:

`AB=√((3-5)^2+(7-3)^2)=√(4+16)=√(20)=2\sqrt5,\\\\A'B'=√((1.5-2.5)^2+(3.5-1.5)^2)=√(1+4)=√(5).`

Therefore, the scale factor for the dilation is given by

`S_c=(A'B')/(AB)=(\sqrt5)/(2\sqrt5)=(1)/(2)=0.5.`

Thus, the required scale factor is (B) 0.5.