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The coordinates of the vertices of trapezoid ABCD are A(−1,4), B(0,2), C(1,2) and D(2,4). ABCD is first rotated 90° counterclockwise, and then translated 3 units right.

Match each coordinate of the final image A′′B′′C′′D′′ in the right column with its correct vertex in the left column.

Pair the coordinates with the letters
(1,1)
(−1,−1)
(1,0)
(−1,2)

A"(?,?)
B"(?,?)
C"(?,?)
D"?,?)

Respuesta :

kudzordzifrancis

Answer:

[tex]A(-1,4)\to A''(-1,-1)[/tex]

[tex]B(0,2)\to B''(1,0)[/tex]

[tex]C(1,2)\to C''(1,1)[/tex]

[tex]D(-2,4)\to D''(-1,2)[/tex]

Step-by-step explanation:

The given trapezoid has vertices at A(−1,4), B(0,2), C(1,2) and D(2,4).

The transformation rule for 90° counterclockwise rotation is

[tex](x,y)\to(-y,x)[/tex]

This implies that:

[tex]A(-1,4)\to A'(-4,-1)[/tex]

[tex]B(0,2)\to B'(-2,0)[/tex]

[tex]C(1,2)\to C'(-2,1)[/tex]

[tex]D(2,4)\to D'(-4,2)[/tex]

This is followed by a translation 3 units to the right.

This also has the rule: [tex](x,y)\to (x+3,y)[/tex]

[tex]A'(-4,-1)\to A''(-1,-1)[/tex]

[tex]B'(-2,0)\to B''(1,0)[/tex]

[tex]C'(-2,1)\to C''(1,1)[/tex]

[tex]D'(-4,2)\to D''(-1,2)[/tex]

Therefore:

[tex]A(-1,4)\to A''(-1,-1)[/tex]

[tex]B(0,2)\to B''(1,0)[/tex]

[tex]C(1,2)\to C''(1,1)[/tex]

[tex]D(-2,4)\to D''(-1,2)[/tex]

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