I need help with these:

Triangle LMN has vertices L(-6,5), M(-4,-3), N(-2,4). Find the coordinates of the vertices of its image after it is reflected over the x-axis and then translated by (-3,0)

a. L(-9,-5), M(-7,3), N(-5,-4)
b. L(-6,-5), M(-4,-3), N(-2,-4)
c. L(-5,-6), M(-7,3), N(-2,-4)
d. L(9,5), M(-4,-3), N(-5,-4)

The vertices of triangle FGH are F(1,1), G(3,-5), H(6,0). Find the coordinates of the vertices after a reflection over the y-axis.

a. J(0,0), K(1,-3), L(7,8)
b. J(0,0(, K(-1,3), L(-7,-8)
c. J(0,0), K(3,1), L(-8,-7)
d. J(0,0), K(-3,-1), L(8,-7)

For the first part, a reflection over the x-axis involves mutliplying the y coord's by -1. Thus
L(-6,5)-> (-6,-5), M(-4,-3)->(-4,3), N(-2,4)->(-2,-4). A translation involves adding (-3,0) to each of these points. Thus L(-6,-5)->(-6,-5)+(-3,0)=(-9,-5). You should be able to finish the others.

For the second one we reflect across the y-axis. This time we negate the x coord's. Thus F(1,1)->(-1,1).
It appears you're missing some kind of translation here. Was it supposed to be translated by (1,-1)? Or is it supposed to be reflected across the origin or some other point or line?

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For the second question, if we reflect triangle FGH over the y-axis, we simply negate the x-coordinates:

F(1,1) becomes (-1,1)
G(3,-5) becomes (-3,-5)
H(6,0) becomes (-6,0)

So the coordinates of the vertices of the reflected triangle are:
J(-1,1), K(-3,-5), L(-6,0)

Therefore, the option that represents the correct coordinates is d. J(0,0), K(-3,-1), L(8,-7).

For the second part, to reflect a point over the y-axis, you need to change the sign of the x-coordinate while keeping the y-coordinate the same.

The given triangle has vertices F(1,1), G(3,-5), and H(6,0). To reflect these points over the y-axis, you need to negate the x-coordinate while keeping the y-coordinate the same.

- F(1,1) reflects to (-1,1)
- G(3,-5) reflects to (-3,-5)
- H(6,0) reflects to (-6,0)

Now, regarding the translation, there is no information given about translation in the question. It seems that the question is only asking about the reflection over the y-axis. Therefore, the correct answer should be:

b. J(-1,1), K(-3,-5), L(-6,0)