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:
[tex]x_O=\dfrac{x_{P_1}+x_{P_2}}{2} \text{ and } y_O=\dfrac{y_{P_1}+y_{P_2}}{2}.[/tex]
Substituting known coordinates, you get:
[tex]-6=\dfrac{-9+x_{P_2}}{2} \text{ and } 5=\dfrac{7+y_{P_2}}{2}.[/tex]
Thus,
[tex]x_{P_2}=-6\cdot 2+9=-12+9=-3,\\ \\y_{P_2}=5\cdot 2-7=10-7=3.[/tex]
Answer: [tex]P_2(-3,3).[/tex]
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
[tex]=(\frac{-9+a}{2},\frac{7+b}{2})[/tex]
now, this point must be (-6,5)
so, we can set it equal
[tex](-6,5)=(\frac{-9+a}{2},\frac{7+b}{2})[/tex]
now, we can compare x-values and y-values
we get
[tex]-6=\frac{-9+a}{2}[/tex]
we can solve for a
[tex]-6*2=-9+a[/tex]
[tex]-12=-9+a[/tex]
[tex]-12+9=-9+a+9[/tex]
[tex]a=-3[/tex]
now, we can compare y-value
[tex]5=\frac{7+b}{2}[/tex]
[tex]5*2=\frac{7+b}{2}*2[/tex]
[tex]10=7+b[/tex]
[tex]10-7=7+b-7[/tex]
[tex]b=3[/tex]
so, we will get
P2=(a,b)
P2=(-3,3)...............Answer
