Pqr fortune-telling formula

The minimum value is 3+ root 5 Q(2.5, 2.5) R(2.0)

Thinking: Finding the minimum perimeter is transformed into finding the shortest line segment between two points.

First, let point P be named point A, which is the symmetrical point about y=x, and then take point A as the perpendicular of the X axis, and the intersection of the perpendicular and the X axis is named as.

Is point r, and the intersection with y=x is named point q, and the connection point QPR. Therefore, the distance from point A to point R is the largest part of the triangle.

Small circumference.

So let the straight line passing through point A and point P be y+x+c=0, substitute point P into c=-5, and the intersection of the straight line and y=x is (2.5, 2.5). Let A(a, b), a+3/2=2.5 b+2=2.5 and find a (2,3), then r is (.