Given a triangle with vertices u(6, −1), w(0, −5), and x(4, −9), and y is the midpoint of segment uw and z is the midpoint of segment wx comma what is the length of yz?

Here we have to use the distance formula

Please see the image attached with the solution , for the figure

Firstly we have to find the length of line segment XU

and the triangle has a property that the length of line segment that connects the midpoint of the two sides is half the length of the third side.

It means here

Length of YZ = half the length of XU

So lets find the length of XU

Now the length of YZ = half of

So length of YZ =

Since there are no images given for the problem, i will define the parabola. a parabola is an open curve that is formed when a cone is sliced parallel to the side of it. the key aspects of a parabola when it is graphed looks like a curve that opens upward, downward, leftward or rightward. it has a latus rectum which is the length of the ends of a curved line. the directrix is the distance between the vertex of a parabola and the line. the vertex is the point where the curve ends.