Question

1. If Triangle ADC is the image of Triangle AEB, which is the proper term for point A?

center of dilation
contraction point
pre-image point
scale factor
2. A segment with endpoints (2, –1) and (4, 2) is dilated to the image segment with endpoints (4, –2) and (8, 4). What is the scale factor for the dilation?
2

4

6

8

Answer 1

Answer: The correct options are (1) (a) Centre of dilation and (2) (a) 2.

Step-by-step explanation: The solutions are as follows:

(1) Given that the triangle AEB is dilated to form triangle ADC. We are to select the correct term for point A.

We see that the point A is a fixed point in the plane about which ΔAEB is dilated to form ΔADC.

Also, we know that a fixed point in the plane about which the figure is dilated is called the centre of dilation. So, A is the centre of dilation.

Thus, (a) centre of dilation is the correct option.

(2) The length of the line segment with end-points (2, -1) and (4, 2) is given by

`l_1=√((4-2)^2+(2+1)^2)=√(4+9)=√(13),`

and the length of the dilated image segment with end-points (4, -2) and (8, 4) is given by

`l_2=√((8-4)^2+(4+2)^2)=√(16+36)=√(52)=2√(13).`

Therefore, the scale factor will be

`S-c=\frac{\textup{length of the dilated segemnt}}{\textup{length of the original segment}}=(2√(13))/(√(13))=2.`

Thus, the correct option is (a) 2.