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Question 62568: Find the midpoint of the line segment PQ for P(4, -3), Q(2, 7)
If M (5, 2) is the midpoint of segment PQ and the coordinates of Q are (3,-3) , find the coordinates of P.
Complete the ordered pairs so that each is a solution to the given linear equation. Present your answer as an ordered pair. 3x - 2y = 12
(a) (-4, ?) (b) (?, -3)
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! Find the midpoint of the line segment PQ for P(4, -3), Q(2, 7)
The midpoint formula is midpoint=((x1+x2)/2,(y1+y2)/2)
(x1,y1)=(4,-3) and (x2,y2)=(2,7)
midpoint=((4+2)/2,(-3+7)/2)
=(6/2,4/2)
=(3,2)
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If M (5, 2) is the midpoint of segment PQ and the coordinates of Q are (3,-3) , find the coordinates of P.
The x coordinate of the midpoint is midpoint=(x1+x2)/2
5=(3+x2)/2
2(5)=2(3+x2)/2
10=3+x2
10-3=3-3+x2
7=x2 This is the x coordinate of P
The y coordinate of the midpoint is midpoint=(y1+y2)/2
2=(-3+y2)/2
2(2)=2(-3+y2)/2
4=-3+y2
4+3=-3+3+y2
7=y2 This is the y coordinate of P
P is (7,7)
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Complete the ordered pairs so that each is a solution to the given linear equation. Present your answer as an ordered pair. 3x - 2y = 12
(a) (-4, ?)
Let x=-4 and solve for y.
3(-4)-2y=12
-12-2y=12
-12+12-2y=12+12
-2y=24
-2y/-2=24/-2
y=-12
(-4,-12)
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(b) (?, -3)
Let y=-3 and solve for x
3x-2(-3)=12
3x+6=12
3x+6-6=12-6
3x=6
3x/3=6/3
x=2
(2,-3)
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Happy Calculating!!!
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