Help - Midpoint

Question

the midpoint of the line segment from P 1 to P 2 is left (-2,5). If P 1=(-9, 8) , what is P 2?

Answer 1

The midpoint formulas are

For the x value: (x₁+x₂)/2=m_x

For the y value: (y₁+y₂)/2=m_y

You are given one point and the midpoint. Plug in the values and solve for the P2 coordinates

(-9+x₂)/2=-2 Multiply both sides of the equation by 2 to clear the fraction

2(-9+x₂)/2=2(-2) Simplify

-9+x₂=-4 Add 9 to both sides

-9+x₂+9=-4+9 Simplify

x₂=5

(8+y₂)/2=5 Multiply both sides of the equation by 2 to clear the fraction

2(8+y₂)/2=2(5) Simplify

8+y₂=10 Subtract 8 from both sides

8+y₂-8=10-8

y₂=2

P₂=(5,2)

Answer 2

P_{1 = (-9,8)}

P_{2 = ?}

Formula for midpoint of a line: (x₂+x₁)/2 , (y₂+y₁)/2

(x₂ and y₂ are the points of P₂ , whereas, x₁ and y₁ are the points of P₁)

Midpoint (x,y) = (-2,5)

Here its given that the X value of the midpoint is -2 and the Y value is 5.

We know that P1 is (-9,8), so x1 is -9 and y1 is 8. we are looking for x2 and y2, so that we can find P2.

Using the formula:

(x2+x1)/2 = -2

(x2 +(-9)) /2 = -2

x2 - 9 = -2*2

x2 = -4 + 9

x2 = 5

(y2+y1)/2 = 5

(y2 + 8) /2 = 5

y2 + 8 = 5*2

y2 + 8 = 10

y2 = 10 - 8

y2 = 2

so P2 is (5,2).

Answer 3

Using the midpoint formula:

M= ( (x1+x2)/2, (y1+y2)/2 ). We know the x and y coordinates of the midpoint from the problem and solve for x2 and y2 in our equations respectively as follows.

(-9+x2)/2= -2 => solving for x2 gives us x2=5

and

(8+y2)/2= 5 => solving for y2 gives us y2=2

Thus the other point must be (5,2)