Question

The midpoint of the line segment from P1 to P2 is (-5,3). If P1 = (-7,4), what is P2?

Answer 1

Answer:

P₂ = (-3, 10)

Step-by-step explanation:

The midpoint, (a, b) = (-5, 3)

The starting point, P₁ = (x₁, y₁) = (-7, 4)

Let P₂ = (x₂, y₂)

The formulae for the coordinates of the midpoint are:

`\begin{gathered} a=(x_1+x_2)/(2) \\ b=(y_1+y_2)/(2) \end{gathered}`

To solve for x₂, substitute a = -5, x₁ = -7 into the formula

`\begin{gathered} -5=(-7+x_2)/(2) \\ -5(2)=-7+x_2 \\ -10=-7+x_2 \\ x_2=-10+7 \\ x_2=-3 \end{gathered}`

To solve for y₂, substitute b = 3, y₁ = -4 into the formula

`\begin{gathered} b=(y_1+y_2)/(2) \\ 3=(-4+y_2)/(2) \\ 2(3)=-4+y_2 \\ 6=-4+y_2 \\ y_2=6+4 \\ y_2=10 \\ \end{gathered}`

Therefore, P₂ = (-3, 10)