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I need help please ....hope someone will answer it... my 4 times posting same question but no answer

What single transformation would show the image of pentagon ABCDE in the same quadrant as the image after pentagon ABCDE is transformed using (x,y) to (-x, y), followed by (x , y) to (x , y - 6)

A(-3,4), B(-5,4), C(-5,2) D(-3,2), E(-2,3)

a) reflection over the x-axis

b) horizontal translation right 7 and vertical translation down 10

c)rotation of 360

d) horizontal translation right 6

Respuesta :

Notice in the first transformation, the y values don't change while the x becomes the opposite, that means the points are reflected across the y axis. 
in the second transformation, notice that the x values don't change, the y values are decreased by 6, so all the points are moved straight downward 6 units. 
To start with, the pentagon is in the second quadrant. You can tell because all the x values are negative and all the y values are positive. Reflected across the y axis, the image is in the first quadrant. shifted down 6 units, all the vertex are in the fourth quadrant.
If we are to use a single transformation to put the original image in the 4th quadrant, the only choice is b). b) puts the pentagon in the 1st, then in the 4th quadrant.
a) puts it in the 3rd quadrant, c) makes the image go back to where it was d)puts the image in the 1st quadrant. 

I tried to answer this question before but I thought the two methods needed to produce two overwrapping images, that is, I thought they needed to end up at exact the same spot. I couldn't figure out how. If the two images just need to be in the same quadrant, my answer is b.
I hope my explanation makes sense. And I hope I am right.
This is a tough one for middle school.

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