Question

Triangle J'K'L' shown on the grid below is a dilation of Triangle JKL using the origin as the center of dilation.


Which scale factor was used to create Triangle J'K'L'?

Answer 1

@mathmale

Answer 2

@rvc

Answer 3

@ShadowLegendX

Answer 4

@dan815 @jigglypuff314 @nincompoop

Answer 5

I was thinking either three or four

Answer 6

@RainbowBrony555

Answer 7

Yes, I think it's 3 or 4 too

Answer 8

Ok is there a way we can narrow it down @RainbowBrony555

Answer 9

Select one:


a.

b. 4

c. 3

d.

Answer 10

Oops that didn't come out right

Answer 11

A. 1/3

D. 1/4

Answer 12

Now, in order to find the dilatation or expansion of a geometric body, which defines a similarity between two geometric bodies.
This last one is a condition for the dilatation of a geometric body and it's representation, let it be in the plane or the three-dimensional space (not proven for n-dimensions).
So, because of that condition we can say that similarity of triangles is applicable, just because they are triangles (I won't go through the proof of this statement but you can try it with two generalized triangles).
So, we will then say that the quotient of their corresponding segments of composition have the same result called the "constant of proportionality", which is exactly the same as the scaling factor for this specific situation.
We will take, for instance, the segments KL and K'L'.
So therefore:
\[\frac{ K'L' }{ KL }=k\]
We will concern ourselves with finding "k", but then we will spot the points K, L, K' and L' and since we are given a grid, which allows us to observe the coordinates of the points we will quickly deduce they are: \(K(9,6)\) \(L(12,9)\) \(K'(3,2)\) \(L'(4,3)\).
So, utilizing the distance formulas:
\[KL=\sqrt{(12-9)^2+(9-6)^2}\]
\[K'L'=\sqrt{(4-3)^2+(3-2)^2}\]
So therefore, "k" will be:
\[k=\frac{ K'L' }{ KL } \iff k=\frac{ \sqrt{(4-3)^2+(3-2)^2} }{ \sqrt{(12-9)^2+(9-6)^2} }\]

Answer 13

The answer would be three then.

Answer 14

Correct me if I am wrong but I believe that if you look at the lines at the base of the triangles and see that they start at two and increase to six you find the difference and then you have your answer 3.

Answer 15

@Owlcoffee

Answer 16

Wait no it was 1/3