Lillyowens420idn
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Triangle J′K′L′ shown on the grid below is a dilation of triangle JKL using the origin as the center of dilation: Two triangles on a grid. First triangle has vertices J 4 and 6, K 2 and 4, and L 6 and 3. Image triangle has vertices J prime 8 and 12, K prime 4 and 8, L prime 12 and 6. Which scale factor was used to create triangle J′K′L′?

Sagot :

MrRoyalidn

When a shape is dilated, the size of the new shape will be different (i.e. bigger or smaller) from the size of the original shape. The scale factor from [tex]\triangle JKL[/tex] to [tex]\triangle J'K'L'[/tex] is 2

Given that:

[tex]\triangle JKL \sim \triangle J'K'L'[/tex] --- similar triangles

Where

[tex]J = (4,6)\\K = (2,4)\\L = (6,3)[/tex]         [tex]J' = (8,12)\\K' = (4,8)\\L' = (12,6)[/tex]

To calculate the scale factor (k) from [tex]\triangle JKL[/tex] to [tex]\triangle J'K'L'[/tex], we simply divide the coordinates of [tex]\triangle J'K'L'[/tex] by the coordinates of [tex]\triangle JKL[/tex]

Using J and J' as points of reference:

[tex]k = \frac{J'}{J}[/tex]

This gives:

[tex]k = \frac{(8,12)}{(4,6)}[/tex]

Factorize

[tex]k = \frac{2 \times (4,6)}{(4,6)}[/tex]

Cancel out the common term

[tex]k = 2[/tex]

Hence, the scale factor from [tex]\triangle JKL[/tex] to [tex]\triangle J'K'L'[/tex] is 2

Read more about scale factors and dilation at:

https://brainly.com/question/2700001

CoughingBloodidn

Answer:

Scale factor of 2 is correct

Step-by-step explanation:

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