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)

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.

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)

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

answer: bearing in mind that a rectangle has a perimeter of length + length + width + width.

step-by-step explanation:

p = perimeter

l = length

x=width

p = 2l + 2x

p = 2(l+x)     < ==== perimeter of the base of the box.