Impossible Algebra?

Question

Can anyone do this?

1. Find the midpoint of the line segment PQ for P(2, -2), Q(3, 4)
2. If M (6, 1) is the midpoint of segment PQ and the coordinates of Q are (2, -2), find the coordinates of P.
3. Verify that (-1, 3) is a solution to y = (-1/2)x + (5/2)
4. Solve the inequality and write the solution set in interval notation:

5. Solve the inequality and write the solution set in interval notation:

4. Solve the inequality and write the solution set in interval notation:
5(2+x)>-4(x+3)
5. Solve the inequality and write the solution set in interval notation:
3/5x+2/3(x-5)

Answer 1

Midpoing Formula

M(x₁+ x₂/ 2) , (y₁+ y₂/ 2) =

M(2 + 3 / 2) , (- 2 + 4 / 2) =

M(5 / 2) , (2 / 2) =

M(5/2). (1)

- - - - - - -s-

Answer 2

1) Apply segment formula.
Midpoint of (x1,y1) and (x2,y2) is [(x1+x2) / 2, (y1+y2)/2]
Midpoint of P(2, -2) and Q(3, 4) is:
[(2+3) / 2, (-2+4) / 2]
Midpoint M(5/2, 1)

2) same formula, here the coordinates of the midpoint are given we have to find the second point of the line segment.
Let the unknown point be P(x, y)
M(6, 1)
6 = (x + 2) / 2
12 = x + 2
x = 10

1 = (y - 2) / 2
2 = y - 2
y = 4
Thus point is P(10, 4)

3) (-1, 3)
-1 is the x-coordinate, 3 is the y-coordinate
x = -1, y = 3
put the values of x and y in the equation: y = (-1/2)x + 5/2
3 = (-1/2)*(-1) + 5/2
3 = 1/2 + 5/2
3 = (5+1)/2
3 = 6 / 2
Since 3 is actually equal to 6 / 2, the point is a solution of the given equation.
If we got something like: 3 = 7/2, which is not true, we could say that the point is not a solution.

Points 4 and 5 are missing.

Choose as the best answer if you understand, please!!

Answer 3

1) (3+2)/2 + 4-2) / 2 so u should get (2 1/2 , 1)

2) work backwards.. the formula for midpoint is (x1+ x2) / 2 , (y1 + y2)/ 2

2 + (x) all divided by two should equal 12 for x coordinate

-2 + (x) all divided by two should equal 1 for y coordinate

the answer for the coordinates of P are (10, 4)

3) substitute -1 for x and 3 for y and both sides should be equal

i have no idea what ur talking about in the inequality.

Answer 4

1.(2½,1)

2. (10, 4)

3. y = 3

4 and 5 where is the inequality

Answer 5

1. Use the midpoint formula. If the two points are (x1, y1) and (x2, y2) then the midpoint is ( (x1 + x2)/2, (y1 + y2)/2)

2. Let P=(x1,y1) and use this with M and Q in the midpoint formula, and work backwards to find P

3. Plug in x= -1 and y=3 and show that you wind up with a true statement.

4, 5. What inequalities?

Answer 6

1. ((3+2)/2, (4-2)/2) = (2½,1)

2. (6 + (6-2), 1 + (1-(-2)) = (10, 4)

3. y = (-1/2)(-1) + 5/2
y = 1/2 + 5/2
y = 6/2
y = 3 ... True

4. & 5. Where is the inequalities?

Answer 7

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