Question

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

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

$l_1=\sqrt{(4-2)^2+(2+1)^2}=\sqrt{4+9}=\sqrt{13},$

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

$l_2=\sqrt{(8-4)^2+(4+2)^2}=\sqrt{16+36}=\sqrt{52}=2\sqrt{13}.$

Therefore, the scale factor will be

$S-c=\dfrac{\textup{length of the dilated segemnt}}{\textup{length of the original segment}}=\dfrac{2\sqrt{13}}{\sqrt{13}}=2.$

Thus, the correct option is (a) 2.