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Line segment RS has endpoints R(– 2, 4) and S (– 4, – 1). Line segment R''S'' has endpoints R'' (3, – 3) and S'' (5, 2). Name the transformations that map line segment RS to line segment R''S''. reflection over the line y = x, followed by a translation (x, y) → (x + 1, y + 1) rotation of 180° about the origin, followed by a translation (x, y) → (x + 1, y + 1) rotation of 90° counterclockwise about the origin, followed by a translation (x, y) → (x + 2, y + 1) translation (x, y) → (x + 1, y + 1), followed by a rotation of 180°counterclockwise about the origin

Respuesta :

MrRoyal

Answer:

Rotation of 180° about the origin,

Followed by a translation (x, y) → (x + 1, y + 1)

Step-by-step explanation:

Given

[tex]R = (-2,4)[/tex]

[tex]S = (-4,-1)[/tex]

[tex]R" = (3,-3)[/tex]

[tex]S" = (5,2)[/tex]

Required

Determine the transformations

From the list of given options (B) answers the question.

Rotation of 180° about the origin,

When a point (x,y) is rotated 180 about the origin, the new point becomes (-x,y)

So:

[tex]R = (-2,4)[/tex]

[tex]S = (-4,-1)[/tex]

becomes

[tex]R' = (2,-4)[/tex]

[tex]S' = (4,1)[/tex]

A translation (x, y) → (x + 1, y + 1)

This implies that 1 is added to the x and y coordinates

So:

[tex]R' = (2,-4)[/tex]

[tex]S' = (4,1)[/tex]

becomes

[tex]R" = (2 + 1,-4 + 1)[/tex]

[tex]R" = (3,-3)[/tex]

[tex]S"=(4 +1,1+1)[/tex]

[tex]S" = (5,2)[/tex]

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