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What are the coordinates of each point after quadrilateral ABCD is reflected across the y-axis and then translated 2 units down? Drag numbers to complete the coordinates. Numbers may be used once, more than once, or not at all. A coordinate plane with three trapezoids. Trapezoid A B C D has coordinates A 1 comma 1, B 2 comma 3, C 4 comma 3, and D 5 comma 1. –5–4–3–2–112345 A'( , ), B'( , ), C'( , ), D'( , )

Sagot :

MrRoyal

Answer:

[tex]A" =(-1,-1)[/tex]    [tex]B" =(-2,1)[/tex]

[tex]C" =(-4,1)[/tex]    [tex]D" =(-5,-1)[/tex]

Step-by-step explanation:

Given

[tex]A = (1,1)[/tex]        [tex]B =(2,3)[/tex]

[tex]C = (4,3)[/tex]        [tex]D = (5,1)[/tex]

Required

The new coordinates after reflected across y-axis and shifted 2 units down

When a point is reflected across the y-axis, the rule is:

[tex](x,y)=>(-x,y)[/tex]

So:

[tex]A = (1,1)[/tex] [tex]=> A' = (-1,1)[/tex]

[tex]B =(2,3)[/tex] [tex]=> B' = (-2,3)[/tex]

[tex]C = (4,3)[/tex] [tex]=> C' = (-4,3)[/tex]

[tex]D = (5,1)[/tex] [tex]=> D' = (-5,1)[/tex]

When a point is translated 2 units down, the rule is:

[tex](x,y) => (x,y-2)[/tex]

So:

[tex]A = (1,1)[/tex] [tex]=> A' = (-1,1)[/tex] [tex]=> A" =(-1,-1)[/tex]

[tex]B =(2,3)[/tex] [tex]=> B' = (-2,3)[/tex] [tex]=> B" =(-2,1)[/tex]

[tex]C = (4,3)[/tex] [tex]=> C' = (-4,3)[/tex][tex]=> C" =(-4,1)[/tex]

[tex]D = (5,1)[/tex] [tex]=> D' = (-5,1)[/tex] [tex]=> D" =(-5,-1)[/tex]

So, the new coordinates are:

[tex]A" =(-1,-1)[/tex]    [tex]B" =(-2,1)[/tex]

[tex]C" =(-4,1)[/tex]    [tex]D" =(-5,-1)[/tex]

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