Question

Apply the dilation D to the polygon with the given vertices. Name the coordinates of the image points. Identify and describe the transformation.

D: (x,y) → (4x,4y)
A (2,1) B (4,1) C (4,-3)


A. This is a dilation about (0, 0) with a scale factor of 0.25; A’(8, 4), B’(16, 4), C’(16, –12).

B. This is a dilation about (0, 0) with a scale factor of 4; A’(8, 4), B’(16, 4), C’(16, –12).

C. This is a dilation about (0, 0) with a scale factor of 0.25; A’(0.5, 0.25), B’(1, 0.25), C’(1, –0.75).

D. This is a dilation about (0, 0) with a scale factor of 4; A’(0.5, 0.25), B’(1, 0.25), C’(1, –0.75).

Answer 1

The question asks to apply a dilation transformation to a polygon with a scale factor of 4. The correct image points after dilation are A'(8, 4), B'(16, 4), C'(16, –12), which means option B is the correct answer.

Step-by-step explanation:

The transformation described in the question is a dilation where every point (x, y) of the polygon is mapped to a new point with coordinates (4x, 4y). Thus, the dilation is about the origin (0, 0) with a scale factor of 4. To find the coordinates of the image points after the transformation, each vertex of the polygon is multiplied by the scale factor:

• A (2,1) becomes A’(2*4, 1*4) = A’(8, 4)
• B (4,1) becomes B’(4*4, 1*4) = B’(16, 4)
• C (4,-3) becomes C’(4*4, -3*4) = C’(16, -12)

The correct answer is therefore option B: This is a dilation about (0, 0) with a scale factor of 4; A’(8, 4), B’(16, 4), C’(16, – 12).

Answer 2

To solve this you just do ehat was done to the coordinates. So x goes from x to 4x do you are mutiplying by 4. and the same goes for y. so your scale factor is 4

2 times 4 is 8 and 1 times 4 is four

A(8,4)

4 times 4 is 16 and 1 times four is four

B(16,4)

Four times four is sixteen and negitive three times four is negitive 12

C(16,-12)

Given the options the answer will be B.