Question

Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates of the other endpoint Q

P(2-6) and M(-3/2, -2)

Answer 1

To find the coordinates of the other endpoint Q, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M between two endpoints P(x₁, y₁) and Q(x₂, y₂) is given by M((x₁ + x₂)/2, (y₁ + y₂)/2).

Step-by-step explanation:

To find the coordinates of the other endpoint Q, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M between two endpoints P(x₁, y₁) and Q(x₂, y₂) is given by M((x₁ + x₂)/2, (y₁ + y₂)/2). Using the given coordinates:

• 
  
• Endpoint P has coordinates P(2, -6).
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• Midpoint M has coordinates M(-3/2, -2).

Substituting the values into the midpoint formula:

M((-3/2 + x₂)/2, (-2 + y₂)/2) = (-3/2, -2)

Simplifying the equation:

(2x₂ - 3)/(2) = -3/2

4x₂ - 6 = -3

4x₂ = 3 - 6

4x₂ = -3

x₂ = -3/4

Therefore, the coordinates of the other endpoint Q are Q(-3/4, y₂).