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.
