Find midpoint M of AB. Solve the diagram below
2 answers:
First, figure out the coordinates of each end-point.
Just read them off of the graph:
A = (9, 11)
B = (-3, -5)
Now, you have to know how to find the midpoint between two given points.
That's easy:
-- The 'x' coordinate of the midpoint is the average of the 'x' coordinates
of the two ends.
-- The 'y' coordinate of the midpoint is the average of the 'y' coordinates
of the two ends.
The 'x' coordinates of the ends are 9 and -3.
Their average is 1/2 of (9 - 3) = 1/2 of (6) = 3 .
The 'y' coordinates of the ends are 11 and -5 .
Their average is 1/2 of (11 - 5) = 1/2 of (6) = 3 .
We have calculated that the midpoint is the point <em>(3, 3)</em> .
I added that to your drawing.
See my attached drawing.
Just read them off of the graph:
A = (9, 11)
B = (-3, -5)
Now, you have to know how to find the midpoint between two given points.
That's easy:
-- The 'x' coordinate of the midpoint is the average of the 'x' coordinates
of the two ends.
-- The 'y' coordinate of the midpoint is the average of the 'y' coordinates
of the two ends.
The 'x' coordinates of the ends are 9 and -3.
Their average is 1/2 of (9 - 3) = 1/2 of (6) = 3 .
The 'y' coordinates of the ends are 11 and -5 .
Their average is 1/2 of (11 - 5) = 1/2 of (6) = 3 .
We have calculated that the midpoint is the point <em>(3, 3)</em> .
I added that to your drawing.
See my attached drawing.
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Answer:
See explanation
Step-by-step explanation:
You have to graph the system of inequalities presented as
Part A:
1. Draw a dotted line (dotted because the sign < is without notion "or equal to"). Select one of two regions by substituting the coordinates of origin into inequality:
Since this inequlity is false, the origin doesn't belong to the shaded region, so you have to shade that part which doesn't contain origin (red part in attached diagram).
2. Draw a solid line (solid because the sign ≥ is with notion "or equal to"). Select one of two regions by substituting the coordinates of origin into inequality:
Since this inequlity is true, the origin belongs to the shaded region, so you have to shade that part which contains origin (blue part in attached diagram).
The intersection of these two regions is the solution area.
Part B:
Plot point (-2,-2). Since this point doesn't belong to the solution area, this is not a solution of the system of two inequalities. You can check it mathematically - substitute x=-2 and y=-2 into the system:
Both inequalities are false, so (-2,-2) doesn't belong to the solution area.
