Dilate the figure below with a scale factor of 1.5 centered at the origin and then rotate the figure 90° clockwise about the origin.

Step-by-step explanation:

Vertices of the quadrilateral are (-4, 1), (-3, 2), (-1, 2) and (-2, 1).

If the given quadrilateral is dilated by ta scale factor of 1.5 about the origin.

Rule for the dilation,

(x, y) → (kx, ky) [k = scale factor]

New vertices of the quadrilateral after the transformation will be,

(-4, 1) → (1.5×4, 1.5×1)

        → (-6, 1.5)

(-3, 2) → (-4.5, 3)

(-1, 2) → (-1.5, 3)

(-2, 1) → (-3, 1.5)

Now the new points are rotated by 90° clockwise about the origin,

Rule for the rotation of the points,

(x, y) → (y, -x)

So the new vertices will be,

(-6, 1.5) → (1.5, 6)

(-4.5, 3) → (3, 4.5)

(-1.5, 3) → (3, 1.5)

(-3, 1.5) → (1.5, 3)

We can plot these points on the graph to form a new (image) quadrilateral.

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