The point (-7, 4) is reflected over the line x= -3. Then, the result point is reflected over the line y = x. Where is the point located after both reflections? A. (-10, 7)
B. (1, 4)
C. (4, -7)
D. (4, 1)

D. (4, 1)

Step-by-step explanation:

When we have a reflection over a line, the perpendicular distance to that line is invariant.

Then, if we have the point

(-7, 4) and we have a reflection over the line x = -3

The distance between the x component and the line is:

I -7 - (-3)I = 4

Then the reflected point will also be at a distance of 4 units to the line x = 3, and this is at the point x = 1.

Then the new point is (1, 4)

Now we do a reflection over the line x = y.

This type of reflection just changes the x-component by the y-component, and the y-component by the x-component.

Then the new point will be (4, 1)

Then the correct option is D.

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

answer: yes i agree that you should not put it on/p>

step-by-step explanation: the reason for this is that it wastes other peoples time and also make them fail as well and that is never good.