Question

#1 series of transformations
follow the series of transformations.
a(5,8) b(1,7) c(2,1) d(4,2)
translate (x,y)→(x - 5,y - 6)
a(0,2) b(-4,1) c(-3,-5) d(-1,-4)
reflect over the x - axis.
a(0,-2) b(-4,-1) c(-3,5) d(-1,4)
rotate 270 degrees. (x,y)→(y,-x)
a(-2,0) b(4, ) c( ) d( )
translate (x,y)→(x + 5,y + 9)
a( ) b( ) c( ) d( )
dilate k = 2
a( ) b( ) c( ) d( )

Explanation:

Step1: Calculate B''' coordinates

For point B''(-4,-1), after 270 - degree rotation (x,y)→(y, - x), we substitute x=-4 and y = - 1. So B''' is (-1,4).

Step2: Calculate C''' coordinates

For point C''(-3,5), substituting x=-3 and y = 5 into (x,y)→(y, - x), we get C'''(5,3).

Step3: Calculate D''' coordinates

For point D''(-1,4), substituting x=-1 and y = 4 into (x,y)→(y, - x), we get D'''(4,1).

Step4: Calculate A'''' coordinates

For point A'''(-2,0), after translation (x,y)→(x + 5,y+9), we substitute x=-2 and y = 0. So A'''' is (-2 + 5,0 + 9)=(3,9).

Step5: Calculate B'''' coordinates

For point B'''(-1,4), substituting x=-1 and y = 4 into (x,y)→(x + 5,y+9), we get B''''(-1 + 5,4 + 9)=(4,13).

Step6: Calculate C'''' coordinates

For point C'''(5,3), substituting x=5 and y = 3 into (x,y)→(x + 5,y+9), we get C''''(5 + 5,3 + 9)=(10,12).

Step7: Calculate D'''' coordinates

For point D'''(4,1), substituting x=4 and y = 1 into (x,y)→(x + 5,y+9), we get D''''(4 + 5,1 + 9)=(9,10).

Step8: Calculate A''''' coordinates

For point A''''(3,9), after dilation with k = 2, we multiply each coordinate by 2. So A''''' is (3×2,9×2)=(6,18).

Step9: Calculate B''''' coordinates

For point B''''(4,13), after dilation with k = 2, we get B'''''(4×2,13×2)=(8,26).

Step10: Calculate C''''' coordinates

For point C''''(10,12), after dilation with k = 2, we get C'''''(10×2,12×2)=(20,24).

Step11: Calculate D''''' coordinates

For point D''''(9,10), after dilation with k = 2, we get D'''''(9×2,10×2)=(18,20).

Answer:

A'''''(6,18), B'''''(8,26), C'''''(20,24), D'''''(18,20)