Question

WILL FAN AND MEDAL!! Dilation problem!!!

Polygon MNOPQ is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image M′N′O′P′Q′. If M = (2, 4) and N = (3, 5), what is the slope of line M'N'?

Answer 1

\[A. \sqrt{2} \]
\[B. 1\]
\[C.\sqrt{3}\]
\[D.\sqrt{\frac{ 1 }{ 2 }}\]

Answer 2

@AccessDenied @sourwing @ganeshie8 @jim_thompson5910 some please help

Answer 3

@saifoo.khan

Answer 4

Tried plotting?

Answer 5

yes

Answer 6

http://www.mathway.com/graph/MjY3MTU

Answer 7

I don't understand how to find the slope

Answer 8

using 2 given points. Could I use the distance formula? @AccessDenied

Answer 9

We're looking for slope, right? Slope between the two dilated points, M' and N'. So if we first found M' and N', we have to use the formula for slope rather than the formula for distance.

Answer 10

okay, with the distance formula I got \[\sqrt{2}\]

Answer 11

\[slope=\frac{ y2-y1 }{ x2-x1}=\frac{ 5-4 }{ 3-2 }=\frac{ 1 }{ 1 }=1\]

Answer 12

Yup, that's the one we'd want to answer the question:
" what is the slope of line M'N'? "
But here we were using M and N, while M' and N' are the already-dilated points. Luckily, if we multiplied everything by a scaling factor like 0.8, it just becomes excess:
\( \dfrac{5 - 4}{3 - 2} \iff \dfrac{5\times 0.8 - 4 \times 0.8}{3 \times 0.8 - 2 \times 0.8} = \dfrac{0.8}{0.8} \dfrac{(5 - 4)}{(3 - 2)} \)

Answer 13

so multiply (5-4) by 0.8? and (3-2) by 0.8?

Answer 14

@AccessDenied I got 1

Answer 15

I agree with slope = 1. :)
What's strange is that most options seem to have a square root involved, as if using distance formula. But the question asks for slope. o.O

Answer 16

That is were they trick you.

Answer 17

I guess it's where they see the 2 given points, and forget about the slope. That's what I done.

Answer 18

Yea, I guess so!
Really if you have integer coordinates and it said "find slope," you wouldn't even need to do work if 3/4 choices were square roots. Slope is all fractions and subtracting, so no square roots unless the coordinates have them... lol

Answer 19

Ill remember that next time :)

Answer 20

It's a good thought for some problems, just don't forget how to do the problem in case they decide to throw a second curve ball (now there's only one square root in the distance problem [square roots can simplify to integers]!). ;)

Answer 21

;) okay, I still have 4 more dilation questions:/

Answer 22

Hm, what's next?

Answer 23

I just posted it