Question

1. a line segment has the endpoints f(-19, -3) and g(15, 19). find the coordinates of its midpoint m.

write the coordinates as decimals or integers.
m = ( , )

1. find the distance between the points (-8.3, 8.9) and (-8.3, -5).

units

1. (overline{jk}) has a midpoint at m(9.5, 13.5). point j is at (10, 11). find the coordinates of point k.

write the coordinates as decimals or integers.
k = ( , )

Explanation:

Step1: Midpoint formula

The midpoint formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). For \(F(-19,-3)\) and \(G(15,19)\), \(x=\frac{-19 + 15}{2}=\frac{-4}{2}=-2\), \(y=\frac{-3+19}{2}=\frac{16}{2}=8\).

Step2: Distance formula (vertical line case)

The distance formula is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Since \(x_1=x_2=-8.3\), \(d=\vert y_2 - y_1\vert=\vert-5 - 8.9\vert=\vert-13.9\vert = 13.9\).

Step3: Midpoint formula (reverse)

Let \(K=(x,y)\). Using midpoint formula \(9.5=\frac{10 + x}{2}\), so \(10+x = 19\), \(x=9\); \(13.5=\frac{11 + y}{2}\), so \(11 + y=27\), \(y = 16\).

Answer:

1. \(M=(-2,8)\)
2. \(13.9\)
3. \(K=(9,16)\)