Question

Point M is the midpoint of overline PQ . The coordinates of point M are (2, 4) . The coordinates of point Q are (12, 10) . What are the coordinates of point P?

Answer 1

Answer:

-8,-2

Step-by-step explanation:

Answer 2

The coordinates of point P are ( -8 , -2 ).

The midpoint of a Line:

• If P$(x_1 , y_1)$ and Q $(x_2 , y_2)$ are the endpoints of the line PQ, then coordinates of midpoint M are given by :
  
  $x = \frac{x_1 +x_2}{2}$   &  $y = \frac{y_1 +y_2}{2}$

How to solve the given question?

• Let P $(x_1 , y_1)$ = (a,b) & Q $(x_2 , y_2)$ = (12,10) and midpoint M(x,y) = (2,4).
  ∴  $x = \frac{x_1 +x_2}{2}$
  ∴  $2 = \frac{x_1 +12}{2}$
  ∴ $4 = 12 + x_1$
  ∴ $x_1 = 4 - 12 = -8$
  Similarly,    $y = \frac{y_1 +y_2}{2}$
  ∴ $4 = \frac{y_1 +10}{2}$
  ∴ $8 = 10 + y_1$
  ∴ $y_1 = 8 - 10 = -2$

Thus the coordinates of point P are (-8 , -2).

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