Question

Which sequence of transformations produces R’S’T’ from RST?

On a coordinate plane, triangle R S T has points (0, 0), (negative 2, 3), (negative 3, 1). Triangle R prime S prime T prime has points (2, 0), (0, negative 3), (negative 1, negative 1).
a 90Degrees clockwise rotation about the origin and then a translation 2 units left
a 90Degrees counterclockwise rotation about the origin and then a translation 2 units right
a translation 2 units left and then a reflection over the y-axis
a translation 2 units right and then a reflection over the x-axis

Answer 1

Answer: B a 90 degree counterclockwise rotation about the origin and then a translation 2 units right

Explanation:

Answer 2

Option D. is the correct transformation.

Explanation:

Coordinates of the given points are R(0, 0), S(-2, 3) and T(-3, 1)

Coordinates of the new points after transformations are R'(2, 0), S'(0, -3) and T'(-1, -1).

Option A.

Rule for 90 degree clockwise rotation about the origin and translation 2 units left is,

(x, y) → (y - 2, -x)

This rule is not applicable for the given transformation.

Option B.

a 90° counterclockwise rotation about the origin and then a translation 2 units right

Rule → (x, y) → (-y + 2, x)

This rule is not applicable for the given transformation.

Option C.

A translation 2 units left and then a reflection over the y axis.

Rule → (x, y) → (-x + 2, y)

This rule is not applicable for the given transformation.

Option D.

A translation 2 units right and then a reflection over the x axis.

Rule → (x, y) → (x + 2, -y)

R(0, 0) → (2, 0)

S(-2, 3) → (0, -3)

T(-3, 1) → (-1, -1)

Option D. is the correct transformation.