Question

find the coordinates of the midpoint m of the segment with the given endpoints. g(3,6) and h(9, - 2) midpoint: m (, ) find the distance between the endpoints. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Find the midpoint

The midpoint formula is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).
For \(G(3,6)\) and \(H(9, - 2)\), \(x_1 = 3,x_2=9,y_1 = 6,y_2=-2\).
\(x\) - coordinate of midpoint: \(\frac{3 + 9}{2}=\frac{12}{2}=6\)
\(y\) - coordinate of midpoint: \(\frac{6+( - 2)}{2}=\frac{4}{2}=2\)

Step2: Find the distance

The distance formula is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute \(x_1 = 3,x_2=9,y_1 = 6,y_2=-2\) into the formula:
\(d=\sqrt{(9 - 3)^2+(-2 - 6)^2}=\sqrt{6^2+(-8)^2}=\sqrt{36 + 64}=\sqrt{100}=10\)

Answer:

Midpoint: \(M(6,2)\)
Distance: \(10\)