Question

In ΔABC, ∠ ABC is a right angle included between AB¯¯¯¯¯ = 3 units and BC¯¯¯¯¯ = 2 units. ΔABC is dilated by a scale factor of 0.5 with point B as the center of dilation, resulting in the image ΔA′B′C′. Which statement about A'B¯¯¯¯¯¯ is true?

A'B¯¯¯¯¯¯ is 1.5 units long and lies on the same line as AB¯¯¯¯¯.

A'B¯¯¯¯¯¯ is 3 units long and lies on the same line as AB¯¯¯¯¯.

A'B¯¯¯¯¯¯ is 1.5 units long but lies on a different line than AB¯¯¯¯¯.

A'B¯¯¯¯¯¯ is 3 units long but lies on a different line than AB¯¯¯¯¯.

Answer 1

Ok. Since the center of dilation is B, the point won't change location, and since it's a point that's part of the triangle, the dilated figure will stay inside the triangle.

Answer 2

What can you say about point A' by knowing what I just told you?

Answer 3

That it lies on the same line. @javierpratdesaba

Answer 4

Perfect. You can now eliminate answers C and D. The next part is length. Since point A' will lie on AB and move towards B (The scale factor is less than 1), it will make A'B' smaller than AB. If you apply the scale factor to the length of AB, what is the answer?

Answer 5

1.5! :) @javierpratdesaba

Answer 6

Amazing work. I can tell you really study hard (hehe)

Answer 7

Thanks so much, I've been doing this online geometry for a while now and it's been hard to understand on my own. I've had help from people who can't figure it out either, so I'm really glad i found a platform that helps me. @javierpratdesaba

Answer 8

I can totally understand you, I am in module five of the same course as you :) It can get pretty tough at times, and remember we're here for you guys :) BTY who is your geometry instructor?

Answer 9

I'm using the system called Plato, through my school. I don't have an instructor or teacher or anything of that nature. I'm on home hospital from my school doing online classes, so I essentially teach myself the best I can. @javierpratdesaba