Hello! Can someone please help me with this question, I'm super confused!

The endpoints of line AB are A(9,4) and B(5,-4). The endpoints of its image after a dilation are A1(6,3) and B1(3,-3). Find the scale factor and explain each of your steps.

look to the similar questions down below

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Steve and I answered this same question way back in 2011

https://www.jiskha.com/display.cgi?id=1324327824

Of course, I'd be happy to help you with that question!

To find the scale factor of the dilation, we can use the formula:

scale factor = (length of image) / (length of original)

First, let's find the length of line AB using the distance formula. The distance formula is:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of A are (9, 4) and the coordinates of B are (5, -4). Using the distance formula, we have:

length of AB = √((5 - 9)^2 + (-4 - 4)^2)
= √((-4)^2 + (-8)^2)
= √(16 + 64)
= √80
= 4√5

Now, let's find the length of the image A1B1. The coordinates of A1 are (6, 3) and the coordinates of B1 are (3, -3). Using the distance formula, we have:

length of A1B1 = √((3 - 6)^2 + (-3 - 3)^2)
= √((-3)^2 + (-6)^2)
= √(9 + 36)
= √45
= 3√5

Finally, we can find the scale factor by dividing the length of the image by the length of the original:

scale factor = (length of image) / (length of original)
= (3√5) / (4√5)
= (3/4) * (√5 / √5)
= 3/4

Therefore, the scale factor of the dilation is 3/4.