Question

The endpoints of a side of a regular pentagon PQRST are R(5, -4) and S(1, -1). Z(6, y) is a point that lies on the line of symmetry that intersects side RS.

What is the value of y? Show your work.

Answer 1

For a pentagon, the line of symmetry perpencularly bisects one side. In this case that side is RS.

Hence this line goes thru the mid point of RS, the mid point of RS is \[(\frac{5+1}{2},\frac{-4-1}{2}) = (3,-2.5)\]

Now the, line goes thru these two points hence the slope is \[\frac{y+2.5}{6-3} = \frac{y+2.5}{3}\]

Slope of RS \[\frac{-4+1}{5-1} = -3/4\]

Hence the line perpendicular to it will have a slope = 4/3
hence, \[\frac{y+2.5}{3} = \frac{4}{3} => y = 1.5\]

Answer 2

thank u

Answer 3

You are welcome :)