Can anyone explain to me how do you get the midpoint of a line segment PQ?

Question

Here is my algebra homework question. If M (-7, -3) is the midpoint of segment PQ and the coordinates of Q are (6, -3), find the coordinates of P.
I need step by step instructions so i can understand this.

Answer 1

M (-7, -3) is the midpoint of segment PQ and the coordinates of Q are (6, -3).
Let the co-ordinates of P be (x,y).
Then, (-7,-3) = ((x+6)/2, (y-3)/2)
=>(x+6)/2 => -7 , (y-3)/2 = -3
=>(x+6) => -14 , (y-3) = -6
=>x => -14-6 , y = -6+3
=>x => -20 , y = -3

So, co-ordinates of point p are (-20, -3)

All the best

Answer 2

midpoint formula

x₁+ x₂/2 , y₁ + y₂/2

since in the midpoint formula a division of 2 was performed to obtail the midpoint coordinates.

The solution is to multiply the midpoint coordinated by 2 to obtain the P

Midpoint = (- 7, - 3)

Q = (6, - 3)

solving for x₂to get the x coordinates of P

- 7 x 2 = 6 + x₂

- 14 = 6 + x₂

- 14 - 6 = 6 + x₂- 6

- 20 = x₂

The answer is x₂= - 20

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solving for y₂ to get the y coordinates of P

- 3 x 2 = 3 + y₂

- 6 = 3 + y₂

- 6 - 3 = 3 + y₂- 3

- 9 = y₂

The answer is y₂= - 9

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The PQ segment is (- 20, - 9)

- - - - - - - - - - - -s-

Answer 3

Remember that to work out the mid point you add the x coordinates together and divide by two

X(mid) = ( X1 + X2) /2

and do the same for the y.

Y(mid) = (Y1 + Y2) /2

this question gives you one of the points and the mid points so just look at the formula above and put in what you have:

X(mid) = ( X1 + X2) /2
-7 = (6 +X2) / 2

So solve for X2 to get the x coordinates of P
-7*2 = 6 + X2
-14 - 6 = X2
-20 = X2

Then do the same for the Y coordinates.

Answer 4

You can ignore -3 has it only show you a horizontal line.

distance between 6 and -7 is 13 (6-[-7])
Therefore -7's position we subtract another 13 and get -20
thus:
-(6-(-7)+7),-3
-20,-3

Draw a line/sketch to understand. It is easier than you thought.

Answer 5

the formula is: x=(x1 + x2)/2, y=(y1 + y2)/2 where x and y are the co-ordinates of the mid-point and x1, y1 are the co-ordinates of point P and x2, y2 are the co-ordinates of the point Q.
So,
-7=(x1 + 6)/2 , -3=(Y1 - 3)/2
x1= -8 , y1= 9
Thus, the point is P(-8,9).

Best of luck for your maths. exam.

Answer 6

if u have points a(X1,Y1) and b(X2,Y2) the midpoint m is

m((X1+X2)/2,(Y1+Y2)/2) so in ur case (Xp+6)/2=-7 so Xp=-20

and (Yp-3)/2=-3 so Yp=-3 so P(-20,-6)