Question

The midpoint of the line segment from P1 to P2 is (-7, 1). If P1=(-5, 9)​, what is P2?

Answer 1

Answer:

Therefore the coordinate of  P₂ is (-3,1)

Step-by-step explanation:

Mid point: The mid-point is a point from where the distance of the end points of a line segment is equal.

The co-ordinate of mid point of (x₁,y₁)  and (x₂,y₂) is $(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$

Here x₁= -5  and y₁= 9

And the coordinate of the mid point is (-7,1).

Let the coordinate of P₂ be (x,y)

Therefore the coordinate of midpoint of P₁ and P₂ is

$(\frac{-7+x}{2} ,\frac{1+y}{2} )$

According to the problem,

$\frac{-7+x}{2} =-5$

$\Rightarrow -7 +x=(-5)\times 2$

$\Rightarrow -7 +x=-10$

$\Rightarrow x=-10+7$

$\Rightarrow x= -3$    

and          

$\frac{1+y}{2} = 1$

$\Rightarrow 1+y= 1\times 2$

$\Rightarrow 1+y=2$

$\Rightarrow y=2-1$

$\Rightarrow y=1$

Therefore the coordinate of  P₂ is (-3,1)