Question

Triangle UVW is drawn with vertices at U(−1, 1), V(0, −4), W(−4, −1). Determine the coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 90° clockwise.

U′(1, −1), V′(0, 4), W′(4, 1)
U′(−1, −1), V′(−4, 0), W′(1, 4)
U′(1, 1), V′(−4, 0), W′(−1, 4)
U′(−1, 1), V′(0, −4), W′(−4, −1)

Answer 1

C. U′(1, 1), V′(−4, 0), W′(−1, 4)

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Use the rule for a rotation of 90° in the xy-plane.

The rule is:

• (x,y) → (y,-x)

Plugging in the coordinates of the preimage into the rule, we can calculate the coordinates of the image as:

• U(-1, 1) → U' (1, 1)
• V(0, - 4) → V' (- 4, 0)
• W(- 4, - 1) → W' (-1, 4)

The matching answer choice is C.

Answer 2

C) U'(1, 1), V'(-4, 0), W'(-1, 4)

Explanation:

Rotation is a transformation that turns an object or a point around a fixed center, changing its orientation while preserving its shape and size.

The mapping rule for a rotation of 90° clockwise about the origin is:

`\large\boxed{(x, y) \rightarrow (y, -x)}`

In other words, switch x and y, and make x negative.

Therefore, if the vertices of triangle UVW are rotated 90° clockwise about the origin, then:

`\begin{aligned}U(-1, 1) &\rightarrow U'(1, 1)\\V(0, -4) &\rightarrow V'(-4, 0)\\W(-4, -1) &\rightarrow W'(-1, 4)\end{aligned}`

Therefore, the coordinates of the vertices for triangle UVW if the preimage is rotated 90° clockwise are:

`\large\boxed{\boxed{\begin{array}{l}U'(1, 1)\\V'(-4, 0)\\W'(-1, 4)\end{array}}}`