Question

The midpoint of the line segment from P1 to P2 is (-6,5). If P1=(-9,7), what is P2?

Answer 1

Let's assume P2 point be (a,b)

P2=(a,b)

The midpoint of the line segment from P1 to P2 is (-6,5)

P1=(-9,7)

so, firstly, we will find mid-point between P1 and P2

we get

`=((-9+a)/(2),(7+b)/(2))`

now, this point must be (-6,5)

so, we can set it equal

`(-6,5)=((-9+a)/(2),(7+b)/(2))`

now, we can compare x-values and y-values

we get

`-6=(-9+a)/(2)`

we can solve for a

`-6*2=-9+a`

`-12=-9+a`

`-12+9=-9+a+9`

`a=-3`

now, we can compare y-value

`5=(7+b)/(2)`

`5*2=(7+b)/(2)*2`

`10=7+b`

`10-7=7+b-7`

`b=3`

so, we will get

P2=(a,b)

P2=(-3,3)...............Answer

Answer 2

Let point O be the midpoint of a segment P₁P₂. Then point O has coordinates (-6,5). You also know coordinates (-9,7) of point P₁.

Use formula for midpoint's coordinates:

`x_O=(x_(P_1)+x_(P_2))/(2) \text{  and  } y_O=(y_(P_1)+y_(P_2))/(2).`

Substituting known coordinates, you get:

`-6=(-9+x_(P_2))/(2) \text{  and  } 5=(7+y_(P_2))/(2).`

Thus,

`x_(P_2)=-6\cdot 2+9=-12+9=-3,\\ \\y_(P_2)=5\cdot 2-7=10-7=3.`

Answer:
`P_2(-3,3).`