Mathematics: 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

1. if triangle adc is the image of triangle aeb,

foreignlove1039

17.01.2022

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.

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lin550

10.03.2021

C 10% Condition.

Step-by-step explanation:

Let's Look at them one by one.

A: Large Enough sample condition.

this is met because 600 students is a good number to carry out a surwey.

B: Randomization, 600 incoming freshman are definitely random.

C: we are left with C so the answer is C.

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