Question

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6 leon designs a fabric pattern using figure stuvw. he dilates figure stuvw using a scale factor of 2 with a center of dilation at vertex v to form figure stuvw. then leon rotates this image 90° clockwise around the origin to form figure stuvw. what are the coordinates of figure stuvw?

Explanation:

Step1: Find coordinates of S'T'U'V'W' after dilation

The center of dilation is at V(1,1). For a point (x,y) dilated with a scale - factor k = 2 centered at (a,b), the formula is (x',y')=(a + k(x - a),b + k(y - b)).

• For S(0,5):
• x'=1+2(0 - 1)=1 - 2=-1
• y'=1+2(5 - 1)=1 + 8 = 9
• For T(3,5):
• x'=1+2(3 - 1)=1+4 = 5
• y'=1+2(5 - 1)=1 + 8 = 9
• For U(3,1):
• x'=1+2(3 - 1)=1+4 = 5
• y'=1+2(1 - 1)=1
• For V(1,1): It remains V'(1,1) since it is the center of dilation.
• For W(1,3):
• x'=1+2(1 - 1)=1
• y'=1+2(3 - 1)=1 + 4 = 5

So the coordinates of S'T'U'V'W' are S'(-1,9), T'(5,9), U'(5,1), V'(1,1), W'(1,5).

Step2: Rotate S'T'U'V'W' 90° clockwise around the origin

The rule for a 90° clock - wise rotation around the origin (x,y)→(y, - x).

• For S'(-1,9): S''(9,1)
• For T'(5,9): T''(9, - 5)
• For U'(5,1): U''(1, - 5)
• For V'(1,1): V''(1, - 1)
• For W'(1,5): W''(5, - 1)

Answer:

S''(9,1), T''(9, - 5), U''(1, - 5), V''(1, - 1), W''(5, - 1)