How to do this question 10?

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1 Answer
Feb 12, 2018

color(blue)(y=-x-12)

Explanation:

All points on the line y=-2x+8 will be transformed by the matrix bb(A)

Any points on this line will have coordinates of the form (k,-2k+8)

:.

((x'),(y'))=((0,-2),(-4,0))[((k),(-2k+8))+((-2),(2))]

color(white)(888888)=((0,-2),(-4,0))((k-2),(-2k+10))

color(white)(888888)=((4k-20),(-4k+8))

i.e.

x'=4k-20 and y'=-4k+8

Eliminating k:

k=(x+20)/4

y=-4((x+20)/4)+8

color(blue)(y=-x-12)

So all images of (x',y') lie on the line y=-x-12.

The line y=-x-12 is the image of y=-2x+8 under the transformation.

Note:

We could have found this line and alternate way. If we had generated two pairs of coordinates using bb(y=-2x+8), and used them in the transformation i.e for bb(X), we would have 2 pairs of coordinates of the image. This would enable us to find the equation of the line.

Example:

From y=-2x+8

For x=3 and x=4

y=2 and y=0color(white)(88) respectively.

Under the transformation we have:

x=-8 and y=-4

x=-4 and y=-8

(y_2-y_1)/(x_2-x_1)=(-8-(-4))/(-4-(-8))=-1

y-(-4)=-(x-(-8))

y+4=-x-8

y=-x-12color(white)(888) as expected.