Question

Point C is at (-9, -2) and point M is at (-1, 4). Point M
is the midpoint of the line segment whose endpoints
are C and D.
What are the coordinates of endpoint D?

Answer 1

Answer:

The coordinates of D is (7, 10)

Explanation:

Let the coordinates of endpoint D be (x, y)

Mid-point formula:

$\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})$

Applying formula:

$\sf (-1, \:4) = (\dfrac{-9+ x}{2},\: \dfrac{-2+y}{2} )$

Comparing found:

$\sf -1 =\dfrac{-9+ x}{2} \quad and \quad \: 4 = \dfrac{-2+y}{2}$

$\sf 2(-1)+9 =x \quad and \quad \: 2(4)+2 =y$

$\sf x = 7 \quad and \quad \: y = 10$

So, coordinates of D is (7, 10)

Answer 2

The answer is (7, 10).

Remember the midpoint formula : $\boxed {M = (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})}$

Finding the x coordinate of D

• x = (x₁ + x₂) ÷ 2
• -1 = (-9 + x₂) ÷ 2
• -2 = -9 + x₂
• x₂ = 7

Finding the y coordinate at D

• y = (y₁ + y₂) ÷ 2
• 4 = (-2 + y₂) ÷ 2
• 8 = -2 + y₂
• y₂ = 10