The midpoint of the line segment from P1 to P2 is (-7,4). If P1=(-7,1) what is P2

Answer 1

Hello Ronnie,

Let's call M (x_M, y_M) the midpoint. The midpoint coordinates are given by the equations:

x_M = (x₁ + x₂)/2

y_M = (y₁ + y₂)/2

Let's start with x_M. You're given x_M = -7 and x₁ = -7 so the equation for x_M can be written as: -7 = (-7+x₂)/2

Multiply both sides of the equation by 2 to get rid of the denominator on the right side and you get:

-14 = -7 + x₂

Add 7 on both sides: -7 = x₂

Moving on to y_M. You're given y_M = 4 and y₁ = 1 so the equation for y_M can be written as: 4 = (1+ y₂)/2

Multiply both sides of the equation by 2 to get rid of the denominator on the right side and you get:

8 = 1 + y₂

Subtract 1 from both sides: 7 = y₂

Let's check by plugging those 2 answers in the midpoint formulas given earlier:

Is -7 = (-7 + -7)/2 true? -7 = -14/2 = -7 TRUE

Is 4 = (1+7)/2 true? 4 = 8/2 = 4 TRUE

So P₂ = (-7, 7)