Question

question 8
knowing that the midpoint of a line segment is (5,1) and one of the endpoints is (2,5), what is the second endpoint of the segment?
(3,4)
(1.5,2)
(8,-3)
(9,16)

Explanation:

Step1: Use mid - point formula

The mid - point formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Let the second endpoint be \((x,y)\), \(x_1=2,y_1 = 5\), mid - point \((\frac{2 + x}{2},\frac{5 + y}{2})=(5,1)\).

Step2: Solve for \(x\)

Set up the equation for \(x\) - coordinate: \(\frac{2+x}{2}=5\). Multiply both sides by \(2\): \(2+x = 10\). Subtract \(2\) from both sides: \(x=10 - 2=8\).

Step3: Solve for \(y\)

Set up the equation for \(y\) - coordinate: \(\frac{5 + y}{2}=1\). Multiply both sides by \(2\): \(5 + y=2\). Subtract \(5\) from both sides: \(y=2-5=-3\).

Answer:

\((8,-3)\) (corresponding to the third option)