Question

question 6 (5 points)
the midpoint of the line segment is (11, -5). if one endpoint of the line segment is (-4, -8), find the coordinates of other endpoint.
(3.5, -6.5)
(15, 3)
(26, -2)
(26, 3)

Explanation:

Step1: Recall the midpoint formula

The midpoint formula is $M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the midpoint $(x_m,y_m)=(11,-5)$ and one endpoint $(x_1,y_1)=(-4,-8)$. We need to find $(x_2,y_2)$.

Step2: Solve for \(x_2\)

Using the \(x\)-coordinate part of the midpoint formula: $11=\frac{-4 + x_2}{2}$. Multiply both sides by 2: $22=-4 + x_2$. Then $x_2=22 + 4=26$.

Step3: Solve for \(y_2\)

Using the \(y\)-coordinate part of the midpoint formula: $-5=\frac{-8 + y_2}{2}$. Multiply both sides by 2: $-10=-8 + y_2$. Then $y_2=-10 + 8 = 3$.

So the other endpoint is \((26,3)\).

Answer:

A. (26, 3)