Question

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

Answer 1

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:

$x_O=\dfrac{x_{P_1}+x_{P_2}}{2} \text{ and } y_O=\dfrac{y_{P_1}+y_{P_2}}{2}.$

Substituting known coordinates, you get:

$-6=\dfrac{-9+x_{P_2}}{2} \text{ and } 5=\dfrac{7+y_{P_2}}{2}.$

Thus,

$x_{P_2}=-6\cdot 2+9=-12+9=-3,\\ \\y_{P_2}=5\cdot 2-7=10-7=3.$

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

Answer 2

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

$=(\frac{-9+a}{2},\frac{7+b}{2})$

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

so, we can set it equal

$(-6,5)=(\frac{-9+a}{2},\frac{7+b}{2})$

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

we get

$-6=\frac{-9+a}{2}$

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

$5=\frac{7+b}{2}$

$5*2=\frac{7+b}{2}*2$

$10=7+b$

$10-7=7+b-7$

$b=3$

so, we will get

P2=(a,b)

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