Question

In a polar coordinate system, the midpoint of the line segment whose endpoints are $\left( 8, \frac{5 \pi}{12} \right)$ and $\left( 8, -\frac{3 \pi}{12} \right)$ is the point $(r, \theta).$ Enter $(r, \theta),$ where $r > 0$ and $0 \le \theta < 2 \pi.$

Answer 1

Explanation:

Given the coordinate points (8, 5π/12) and (-3, π/12)

The midpoint is expressed using the formula

M(X,Y) = {(x1+x2)/2, (,y1+y2)/2}

X = x1+x2/2

X = 8-3/2

X = 5/2

Y = y1+y2/2

Y = (5π/12+π/12)/2

Y = (6π/12)/2

Y = 6π/24

Y = π/4

Hence the required coordinate is at(2.5, π/4)