You are given rectangle ABCD on the grid shown and are told that the figure is to be dilated from the origin, but you are not told by what factor. Which COULD be the new coordinates of point D?

A) (-8, -4)
B) (-2, -2)
C) (-2, -4)
D) (2, 4)

The new coordinates of point D(-4, -4) after the dilation by a scale factor of 1/2 will be: D'(-2, -2)

Step-by-step explanation:

The rectangle ABCD on the grid shown is attached below.

From the grid, it is clear that the coordinates of point D are (-4, -4)

i.e. D(-4, -4)

As we are told that the figure is to be dilated from the origin.

A dilation tends to stretch or shrink the original figure, depending upon scale factor.

When we dilate a figure from the origin by any scale factor, the new coordinates of the image can be obtained by multiplying the scale factor with the coordinates of the original object/figure.

As the the coordinates of point D are (-4, -4). If we dilate the figure by a scale factor of 1/2, the new new coordinates of point D would be:

P(x, y)       →   P'(1/2x, 1/2y)

D(-4, -4)    →   D'(-4/2, -4/2) or D'(-2, -2)

Therefore, the new coordinates of point D(-4, -4) after the dilation by a scale factor of 1/2 will be: D'(-2, -2)

step-by-step explanation:

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,