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1. What are the coordinates of the vertices of triangle J"K"L"? 2. Write ONE algebraic rule that represents triangle JKL being translated to triangle J"K"L".

1. What are the coordinates of the vertices of triangle J"K"L"? 2. Write-example-1
User AmaJayJB
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1 Answer

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The triangle JKL has vertices J(-3,-3), K(-4,2), and L(2,1)

1) This triangle was first translated using the rule:

(x,y) → (x+2,y-3)

This means it was translated 2 units to the right and 3 units down.

JKL → J'K'L'

J(-3,-3) → J'(-3+2,-3-3) = (-1,-6)

K(-4,2) → K'(-4+2,2-3) = (-2,-1)

L(2,1) → L'(2+2,1-3) = (4,-2)

The resulting triangle J'K'L' has vertices J'(-1,-6), K'(-2,-1), and L'(4,-2)

2) The triangle J'K'L' was translated using the algebraic rule

(x,y) → (x-2,y-1)

This indicates it was translated 2 units to the left and one unit down.

The translation is

J'K'L' → J''K''L''

J'(-1,-6) → J''(-1-2,-6-1) = (-3,-7)

K'(-2,-1) → K''(-2-2,-1-1) = (-4,-2)

L'(4,-2) → L''(4-2,-2-1) = (2,-3)

The triangle J''K''L'' has vertices J''(-3,-7), K''(-4,-2), and L''(2,-3)

To determine one algebraic rule that represents the translation from JKL to J''K''L'' directly, you have to compare the coordinates of the vertices of both triangles:

JKL → J''K''L''

J(-3,-3) → J''(-3,-7)

K(-4,2) → K''(-4,-2)

L(2,1) → L''(2,-3)

You have to compare the x-coordinates and the y-coordinates of both triangles.

If you compare the x-coordinates you will notice that they are the same, this means that to make a direct translation from JKL to J''K''L'' you don't have to make any horizontal movements.

If you compare the y-coordinates you will see that they are different, so between both triangles, there was a vertical movement done. To determine the length of said movement, you have to calculate the difference between the y-coordinate of one vertex of J''K''L'' and the corresponding y-coordinate of the vertex of JKL.

For example compare J(-3,-3) and J''(-3,-7)


y_(J^(\doubleprime))-y_J=-7-(-3)=-4

→ So we can conclude that to move JKL to J''K''L'' you have to make a vertical translation 4 units down. The algebraic rule that represents this translation is

(x,y) → (x,y-4)

User Denny Weinberg
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