You are given rectangle ABCD on the grid shown and are told that the figure is moved two units. The person fails to tell you in what direction. Which COULD be the new coordinates of point D?

a. (-6,-4)

b. (-1,-4)

c. (-2,-2)

d. (4,-4)

Option a. (-6,-4)

Step-by-step explanation:

The coordinates of point D from the figure is (-4,-4)

The all possible cases to move the figure 2 units is as following:

By checking the given options, we will find that:

The options b,c and d is not at the previous possible cases

So, the answer is option a. (-6,-4)

Which mean the figure is moved two units left

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be