Question

A rectangle has vertices (8, 6), (4, 6), (8, −4), and (4, −4). What are the coordinates after dilating from the origin by a scale factor of 1.5?


A (12, 9), (6, 9), (12, −6), (6, −6) B (16, 12), (8, 12), (16, −8), (8, −8)
C (10, 8), (5, 8), (10, −5), (5, −5) D (9, 6), (3, 6), (9, −3), (3, −3)

Answer 1

Answer:

The coordinates of A(8, 6), B(4, 6), C(8, −4), and D(4, −4) after dilating from the origin by a scale factor of 1.5 will be: A'(12, 9), B'(6, 9), C'(12, -6), D'(6, -6)

Step-by-step explanation:

When we dilate a figure from the origin by a scale factor of 1.5, it means we will multiply the coordinates of the original figure with 1.5.

• As the scale factor is 1.5 which is > 1, therefore the image will be enlarged.

so

As the rectangle has vertices A(8, 6), B(4, 6), C(8, −4), and D(4, −4)

The coordinates after dilating from the origin by a scale factor of 1.5 will be:

P(x, y)        →          P' (1.5x, 1.5y)

A(8, 6)        →          A'(8×1.5, 6×1.5) = A'(12, 9)

B(4, 6)        →          B'(4×1.5, 6×1.5) = B'(6, 9)

C(8, -4)        →         C'(8×1.5, -4×1.5) = C'(12, -6)

D(4, -4)        →          D'(4×1.5, -4×1.5) = D'(6, -6)

Therefore, the coordinates of A(8, 6), B(4, 6), C(8, −4), and D(4, −4) after dilating from the origin by a scale factor of 1.5 will be: A'(12, 9), B'(6, 9), C'(12, -6), D'(6, -6)